THE  PURCHASING  POWER  OF  MONEY 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON   •    CHICAGO 
SAN    FRANCISCO 

MACMILLAN   &  CO.,  Limited 

LONDON   •    BOMBAY    •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


THE  PURCHASING  POWER 
OF   MONEY 

ITS    DETERMINATION 

AND    RELATION    TO    CREDIT 

INTEREST  AND   CRISES 

BY 
mVING  FISHER 

morassoR  of  political  economt  in  tale  UNIVKBSITT 

ASSISTED    BY 

HARRY   G.    BROWN 

nrSTKUCTOB   IN   POLITICAL  ECONOMY   IN   TALB   UNIVERSITT 


HEW  AMU   JIFVI3II'    EOiTION 


466  66 

Nein  gork 
THE   MACMILLAN   COMPANY 

1920 

AU  rights  reserved 


CiOPTSraHT,  Iffll, 
By  the   MACMILLAN   COMPAlTr. 


Set  up  and  electrotyped.    Published  March,  igit. 


Nodvaoli  9rni« 

J.  S.  Gashing  Co.  —  Berwick  dc  Smith  0*. 

Norwood,  Mass.,  U.S.A. 


2-2-3 


^S5p 


dc-p  ■  > 


Co 

THE    MEMORY    OF 

SIMON   NEWCOMB 

6BEAT    SCIENTIST,    INSPIRING    FRIEND, 

PIONEER   IN   THE   STUDY 

OF 

**  SOCIETARY    circulation" 


PREFACE   TO   THE    FIRST   EDITION 

The  purpose  of  this  book  is  to  set  forth  the  principles 
determining  the  purchasing  power  of  money  and  to 
apply  those  principles  to  the  study  of  historical  changes 
in  that  purchasing  power,  including  in  particular  the 
recent  change  in  "  the  cost  of  living,"  which  has  aroused 
world-wide  discussion. 

If  the  principles  here  advocated  are  correct,  the  pur- 
chasing power  of  money  —  or  its  reciprocal,  the  level  of 
prices  —  depends  exclusively  on  five  definite  factors : 
(1)  the  volume  of  money  in  circulation ;  (2)  its  velocity 
of  circulation  ;  (3)  the  volume  of  bank  deposits  subject 
to  check ;  (4)  its  velocity ;  and  (5)  the  volume  of  trade. 
Each  of  these  five  magnitudes  is  extremely  definite,  and 
their  relation  to  the  purchasing  power  of  money  is  defi- 
nitely expressed  by  an  "equation  of  exchange."  In  my 
opinion,  the  branch  of  economics  which  treats  of  these 
five  regulators  of  purchasing  power  ought  to  be  recog- 
nized and  ultimately  will  be  recognized  as  an  exact 
science,  capable  of  precise  formulation,  demonstration, 
I  and  statistical  verification. 

The  main  contentions  of  this  book  are  at  bottom  simply 
a  restatement  and  amplification  of  the  old  "quantity 
theory  "  of  money.  With  certain  corrections  in  the  usual 
statements  of  that  theory,  it  may  still  be  called  funda- 
mentally sound.  What  has  long  been  needed  is  a  candid 
reexamination  and  revision  of  that  venerable  theory  rather 
than  its  repudiation. 

Yet  in  the  voluminous  literature  on  money,  there  seems 
to  be  very  little  that  approaches  accurate  formulation  and 


VIU  PREFACE    TO   THE    FIRST   EDITION 

rigorous  demonstration,  —  whether  theoretical  or  statis- 
tical. 

In  making  this  attempt  at  reconstruction,  I  have  the 
satisfaction  of  finding  myself  for  once  a  conservative 
rather  than  a  radical  in  economic  theory.  It  has  seemed 
to  me  a  scandal  that  academic  economists  have,  through 
outside  clamor,  been  led  into  disagreements  over  the 
fundamental  propositions  concerning  money.  This  is  due 
to  the  confusion  in  which  the  subject  has  been  thrown 
by  reason  of  the  political  controversies  with  which  it  has 
become  entangled. 

As  some  one  has  said,  it  would  seem  that  even  the 
theorems  of  Euclid  would  be  challenged  and  doubted 
if  they  should  be  appealed  to  by  one  political  party  as 
against  another.  At  any  rate,  since  the  "quantity 
theory "  has  become  the  subject  of  political  dispute,  it 
has  lost  prestige  and  has  even  come  to  be  regarded  by 
many  as  an  exploded  fallacy.  The  attempts  by  pro- 
moters of  unsound  money  to  make  an  improper  use  of  the 
quantity  theory  —  as  in  the  first  Bryan  campaign  —  led 
many  sound  money  men  to  the  utter  repudiation  of  the 
quantity  theory.  The  consequence  has  been  that,  espe- 
cially in  America,  the  quantity  theory  needs  to  be  rein- 
'  troduced  into  general  knowledge. 

Besides  aiming  to  set  forth  the  principles  affecting  the 
purchasing  power  of  money,  this  book  aims  to  illustrate 
and  verify  those  principles  by  historical  facts  and  statis- 
tics. In  particular,  the  recent  rise  in  prices  is  examined 
in  detail  and  traced  to  its  several  causes. 

The  study  of  the  principles  and  facts  concerning  the 
purchasing  power  of  money  is  of  far  more  than  academic 
interest.  Such  questions  affect  the  welfare  of  every  in- 
habitant of  the  civilized  world.  At  each  turn  of  the  tide 
of  prices,  millions  of  persons  are  benefited  and  other 
millions  are  injured. 


PREFACE    TO   THE    FIRST   EDITION  IX 

For  a  hundred  years  the  world  has  been  suffering  from 
periodic  changes  in  the  level  of  prices,  producing  alter- 
nate crises  and  depressions  of  trade.  Only  by  knowledge, 
both  of  the  principles  and  of  the  facts  involved,  can  such 
fluctuations  in  future  be  prevented  or  mitigated,  and  only 
by  such  knowledge  can  the  losses  which  they  entail  be 
avoided  or  reduced.  It  is  not  too  much  to  say  that  the 
evils  of  a  variable  monetary  standard  are  among  the  most 
serious  economic  evils  with  which  civilization  has  to  deal ; 
and  the  practical  problem  of  finding  a  solution  of  the  dif- 
ficulty is  of  international  extent  and  importance.  I  have 
proposed,  very  tentatively,  a  remedy  for  the  evils  of  mon- 
etary instability.  But  the  time  is  not  yet  ripe  for  the 
acceptance  of  any  working  plan.  What  is  at  present  most 
needed  is  a  clear  and  general  public  understanding  of 
principles  and  facts. 

Toward  such  an  end  this  book  aims  to  contribute  :  — 

1.  A  reconstruction  of  the  quantity  theory. 

2.  A  discussion  of  the  best  form  of  index  number. 

3.  Some  mechanical  methods  of  representing  visually 
the  determination  of  the  level  of  prices. 

4.  A  practical  method  of  estimating  the  velocity  of 
circulation  of  money. 

5.  The  ascertainment  statistically  of  the  bank  deposits 
in  the  United  States  which  are  subject  to  check,  as  distinct 
from  "  individual  deposits,"  as  usually  published. 

6.  An  improved  statistical  evaluation  of  the  volume 
of  trade,  as  well  as  of  the  remaining  elements  in  the 
equation  of  exchange. 

7.  A  thorough  statistical  verification  of  the  (recon- 
structed) quantity  theory  of  money. 

As  it  is  quite  impossible  to  do  justice  to  some  of  these 
subjects  without  the  use  of  mathematics,  these  have  been 
freely  introduced,  but   have   been   relegated,  so   far   as 


X  PREFACE    TO   THE    FIRST   EDITION 

possible,  to  Appendices.  This  plan,  which  is  in  accord- 
ance with  that  previously  adopted  in  The  Nature  of  Cap- 
ital and  Income  and  The  Rate  of  Interest,  leaves  the  text 
almost  wholly  nonmathematical. 

Most  of  the  statistical  results  review  and  confirm  the 
conclusions  of  Professor  Kemmerer  in  his  valuable  Money 
and  Credit  Instruments  in  their  Relation  to  General  Prices, 
which  appeared  while  the  present  book  was  in  course 
of  construction.  I  am  greatly  indebted  to  Professor 
Kemmerer  for  reading  the  entire  manuscript  and  for 
much  valuable  criticism  throughout. 

My  thanks  are  due  to  Professor  F.  Y.  Edgeworth  of 
All  Souls'  College,  Oxford,  and  to  Professor  A.  W.  Flux 
of  Manchester  for  kindly  looking  through  the  manuscript 
of  the  Appendix  on  index  numbers  and  for  suggestions 
and  criticisms. 

To  Dr.  A.  Piatt  Andrew,  now  Assistant  Secretary  of 
the  Treasury,  my  thanks  are  due  for  his  kindness,  as 
Special  Assistant  to  the  National  Monetary  Commission, 
in  putting  the  resources  of  that  Commission  at  my  dis- 
posal, and  in  working  out,  from  the  records  of  the  office 
of  the  Comptroller  of  the  Currency,  the  volume  of  deposits 
subject  to  check  at  various  dates  in  the  past.  For  cooper- 
ation in  carrying  out  these  same  calculations,  I  am  like- 
wise indebted  to  Mr.  Lawrence  O.  Murray,  Comptroller 
of  the  Currency.  These  valuable  figures  are  the  first  of 
their  kind. 

To  Mr.  Gilpin  of  the  New  York  Clearing  House,  my 
thanks  are  due  for  his  kindness  in  furnishing  various 
figures  asked  for  and  cited  specifically  in  the  text. 

To  Mr.  Richard  M.  Hurd,  President  of  the  Lawyers 
Mortgage  Co.,  I  am  indebted  for  reading  parts  of  the 
manuscript  and  for  valuable  criticism. 

To  Mr.  John  O.  Perrin,  President  of  the  American 
National  Bank  of  Indianapolis,  I  am  i^idebted  for  statistics 


PREFACE   TO   THE    FIRST   EDITION  XI 

of  the  "activity"  of  bank  accounts  in  liis  bank,  and  for 
similar  figures  I  am  indebted  to  the  officers  of  the  National 
New  Haven  Bank  and  the  City  Bank  of  New  Haven. 

My  thanks  are  due  to  the  Economic  Journal  for  permis- 
sion to  use  unaltered  some  parts  of  my  article  on  "The 
Mechanics  of  Bimetallism,"  which  first  appeared  in  that 
journal  in  1894. 

My  thanks  are  due  to  the  Journal  of  the  Royal  Statistical 
Society  for  similar  permission  with  reference  to  my  article 
on  "A  Practical  Method  for  estimating  the  Velocity  of 
Circulation  of  Money,"  which  appeared  in  December, 
1909. 

A  number  of  my  students  have  rendered  valuable 
service  in  gathering  and  coordinating  statistics.  I  would 
especially  mention  Mr.  Seimin  Inaoka,  Mr.  Morgan  Porter, 
Mr.  N.  S.  Fineberg,  Mr.  W.  E.  Lagerquist,  now  in- 
structor at  Cornell  Universit}'-,  Messrs.  G.  S.  and  L.  A. 
Dole,  Dr.  John  Bauer,  now  assistant  professor  at  Cornell 
University,  Dr.  John  Kerr  Towles,  now  instructor  at  the 
University  of  Illinois,  Dr.  A.  S.  Field,  now  instructor  at 
Dartmouth  College,  Mr.  A.  G.  Boesel,  Mr.  W.  F.  Hicker- 
nell,  Mr.  Yasuyiro  Hayakawa,  Mr.  Chester  A.  Phillips, 
and  Mr.  R.  N.  Griswold.  Mr.  Griswold  performed  the 
lengthy  calculations  involved  in  ascertaining  an  index 
of  the  volume  of  trade. 

There  are  two  persons  to  whom  I  am  more  indebted 
than  to  any  others.  These  are  my  brother,  Mr.  Her- 
bert W.  Fisher,  and  my  colleague.  Dr.  Harry  G.  Brown. 

To  my  brother  my  thanks  are  due  for  a  most  searching 
criticism  of  the  whole  book  from  the  standpoint  of  peda- 
gogical exposition,  and  to  Mr.  Brown  for  general  criticism 
and  suggestions  as  well  as  for  detailed  work  throughout. 
In  recognition  of  Mr.  Brown's  assistance,  I  have  placed 

his  name  on  the  title-page. 

IRVING  FISHER. 
Yale  University,  February,  1911. 


PREFACE   TO   THE   SECOND   EDITION 

The  second  edition  is  a  reprint  of  the  first  with  the  fol- 
lowing changes :  — 

1.  Correction  of  occasional  misprints. 

2.  Addition  of  data  for  1910,  1911,  and  1912,  in  the 
tables  on  pages  301,  317,  and  the  diagram  between  pages 
306  and  307. 

3.  A  change  in  Figure  1  (page  13)  to  make  it  conform 
to  the  facts  for  1912. 

4.  Changes  in  the  table  on  page  147  with  accompany- 
ing text  to  make  the  data  correspond  to  the  facts  for  1912. 

5.  The  insertion  of  an  addendum  on  pages  492-493, 
giving  the  revised  figures  for  deposits  subject  to  check  as 
calculated  by  Professor  Wesley  Clair  Mitchell. 

6.  An  appendix  to  the  second  edition  (page  494  ff.)  on 
"standardizing  the  dollar." 

For  corrections  of  misprints  and  various  helpful  criti- 
cisms of  the  first  edition  I  am  under  great  obligations  to  a 
number  of  friends  and  correspondents  and  particularly  to 
Major  W.  E.  McKechnie,  of  the  Indian  Medical  Service, 
Etawah,  United  Provinces,  India ;  Professor  Warren  M. 
Persons,  Colorado  College,  Colorado  Springs,  Colo. ;  Mr. 
J.  M.  Keynes,  Editor,  Economic  Journal,  Kings  College, 
Cambridge  ;  Carl  Snyder,  author,  New  York  City ;  James 
Bonar,  Deputy  Master  of  the  Royal  Mint,  Ottawa,  Canada ; 
Professor  Allyn  A.  Young,  Washington  University,  St. 
Louis,  Mo.;  Professor  Stephen  Bauer,  Director,  Interna- 
tional Office  of  Labor  Legislation,  Basle,  Switzerland ; 
Professor  Wesley  Clair  Mitchell,  New  York  City  ;  Pro- 
fessor O.  M.  W.  Sprague,  Harvard  University. 


PREFACE   TO  THE   SECOND   EDITION  XUl 

I  have  endeavored  to  avoid  disturbing  the  plates  of  the 
first  edition  more  than  was  absolutely  necessary.  Other- 
wise I  should  have  been  glad  to  incorporate  some  changes 
to  make  use  of  some  valuable  but  general  criticisms.  In 
particular  I  should  have  liked  to  modify  somewhat  the 
statement  of  the  theory  of  crises  in  Chapter  IV  and  in 
Chapter  XI  to  make  use  of  the  helpful  criticism  of  Miss 
Minnie  Throop  England,  of  the  University  of  Nebraska, 
in  The  Quarterly  Journal  of  Economics^  November,  1912 ; 
also  to  meet  a  criticism  of  Mr.  Keynes'  to  the  effect 
that,  while  my  book  shows  that  the  changes  in  the  quantity 
of  money  do  affect  the  price  level,  it  does  not  show  how 
they  do  so.  To  those  who  feel  the  need  of  a  more  defi- 
nite picture  of  how  the  price  level  is  affected  by  a  change 
in  the  quantity  of  money  I  refer  the  reader  to  my  Ele- 
mentary Principles  of  Economics^  pages  242-247,  and  to 
other  writers  on  this  subject,  particularly  Cairns. 

IRVING  FISHER. 


SUGGESTIONS  TO  READERS 

1.  The  general  reader  will  be  chiefly  interested  in 
Chapters  I-VIII. 

2.  The  cursory  reader  will  find  the  gist  of  the  book  in 
Chapter  II. 

3.  Objectors  to  the  quantity  theory  will  find  their  theo- 
retical and  statistical  objections  discussed  in  Chapters 
VIII  and  XII  respectively. 

4.  Studeyits  of  financial  history  should  read  Chapter  XII. 

5.  Currency  reformers  should  read  Chapter  XIII. 

6.  The  appendices  are  addressed  mainly  (though  not 
exclusively)  to  mathematical  economists^  for  whom  the  chief 
interest  will  probably  lie  with  the  Appendix  to  Chapter 
X,  on  Index  Numbers,  (which  should  be  read  as  a  whole,) 
and  §  6  of  the  Appendix  to  Chapter  XII,  on  the  Method 
of  Determining  Velocity  of  Circulation. 

7.  The  remainder  of  the  Appendix  to  Chapter  XII  is 
supplied  chiefly  in  order  that  statistical  critics  may  be  en- 
abled to  verify  the  processes  described  in  the  text. 

8.  Chapter  X  and  its  Appendix  are  of  chief  interest  to 
students  of  index  numbers^  a  subject  as  fascinating  to  some 
as  it  is  dr}'-  to  others. 

9.  The  analytical  table  of  contents,  the  index,  and  the 
running  page  headings  have  been  constructed  with  espe- 
cial reference  to  the  varying  needs  of  different  classes  of 
readers. 

The  book  is,  however,  designed  to  constitute  a  complete 
whole,  and  it  is  hoped  that  as  many  as  possible  of  those 
who  approach  it  from  special  viewpoints  may,  in  the  end, 
read  it  aU. 


SUMMARY   OF  CONTENTS 

OHAPTBB  PAGB 

I.    Primary  Definitions 1  » 

II.     Purchasing  Power  of  Monet  as  belated  to  the  "Equa- 
tion OF  Exchange  " 8  ^ 

in.    Influence  of  Deposit  Currenct  on  the  Equation  and 

therefore  on  Purchasing  Power 33  ~. 

IV.     Disturbance   of  Equation   and   of  Purchasing   Power 

DURING  Transition  Periods 55  -«. 

v.     Indirect  Influences  on  Purchasing  Power     .        .        .74" 

VI.    Indirect  Influences  (Continued) 90 

Vn.     Influence  of  Monetary  Systems  on  Purchasing  Power  112 
VIII.     Influence  of  Quantity  of  Money  and  Other  Factors 

ON  Purchasing  Power  and  on  Each  Other          .        .  149 
IX.    The  Dispersion  of  Prices  makes  necessary  an  Index 

OF  Purchasing  Power 184 

X.     The  Best  Index  Numbers  of  Purchasing  Power    .        .  198 

XL     Statistical  Verification.     General  Historical  Review  234    - 

Xll.     Statistical  Verification.     Recent  Years        .        ,        .  276    '' 

Xlll.     The  Problem  of  making  Purchasing  Power  more  Stable  319    y 

Appendix  to  Chapter  II 349 

Appendix  to  Chapter  III        .        .         ......  367 

Appendix  to  Chapter  V         ........  370 

Appendix  to  Chapter  VI.        .••••..  372 

Appendix  to  Chapter  VII      .••.•.«.  376 

Appendix  to  Chapter  VIII    .        ..•••..  379 

Appendix  to  Chapter  X         .••••••.  885 

Appendix  to  Chapter  XII     ..••■••.  430 


XV 


ANALYTICAL  TABLE  OF  CONTENTS 

CHAPTER  I 

FrIMART   DEFmiTIOMS 

PAOK 

§  1.   Wealth  and  exchange •        .        1 

§  2.    Exchangeable  goods 4 

§  3.   Circulation  of  money  against  goods 6 

CHAPTER  II 

Pdrchasing  Power  of  Monet  as  related  to  thb  Equation 
OF  Exchange 


§  1.  The  various  circulating  media    .... 

§  2.  The  equation  of  exchange  arithmetically  expressed 

§  3.  The  equation  of  exchange  mechanically  expressed 

§  4.  The  equation  of  exchange  algebraically  expressed 

§  5.  Couclusiou  and  illustrations      .... 


8 

14 
21 

24 
28 


CHAPTER  m 
Influence  of  Deposit  Currency  on  the  Equation 

AND    therefore    ON   PURCHASING   POWEB 

§  1.   The  mystery  of  circulating  credit 33 

§  2.   The  basis  of  circulating  credit 40 

§3.  Banking  limitations    .         .         .         .         .         .         .         ,         .42 

§  4,  The  revised  equation  of  exchange       .         .        .         ...      47 

§  5.  Deposit  currency  normally  proportioned  to  money    ...      49 

§  6.    Summary 63 

CHAPTER  IV 

Disturbance  of  Equation  and  of  Purchasing  Power  during 
Transition  Periods 

§  1.  Tardiness  of  interest  adjustment  to  price  movements         .        .  55 

§  2.  How  a  rise  of  prices  generates  a  further  rise      .        .        .        .  58 

§  3.  Extent  of  disturbances  in  equation     .         .         ....  61 

§  4.  How  a  rise  of  prices  culminates  in  a  crisis         ....  64 


XVIU  ANALYTICAL  TABLE   OP  CONTENTS 

PAOB 

§  5.  Completion  of  the  credit  cycle 67 

§  6.  Summary 72 


CHAPTER  V 

Indirect  Influences  on  Purchasing  Power 

§  1.   Influence  of  conditions  of  production  and  consumption  on 

trade  and  therefore  on  prices         .        .  ...       74 

§  2.    Influence  of  conditions  connecting  producers  and  consumers 

on  trade  and  therefore  on  prices 77 

§  3.   Influence  of  individual  habits  on  velocities  of  circulation  and 

therefore  on  prices 79 

§  4.   Influence  of  systems  of  payment  on  velocities  of  circulation 

and  therefore  on  prices         .         .        .         ....      83 

§  5.   Influence  of  general  causes  on  velocities  of  circulation  and 

therefore  on  prices        ........      87 

§  6.  Influences  on  the  volume  of  deposits  subject  to  check  and 

therefore  on  prices 88 


CHAPTER  VI 
Indirect  Influences  (Continued) 

§  1.  Influence  of  foreign  trade  on  the  quantity  of  money  and  there- 
fore on  prices 90 

§  2.   Influence  of  melting  and  minting  on  the  quantity  of  money 

and  therefore  on  prices 96 

§  3.  Influence  of  the  production  and  consumption  of  money  metals 

on  the  quantity  of  money  and  therefore  on  prices        .        .      99 

§  4.   Mechanical  illustration  of  these  influences       ....    104 


CHAPTER  Vn 
Influence  of  Monetary  Systems  on  Purchasing  Powbb 

§  1.   Gresham's  Law 112 

§  2.   Cases  when  bimetallism  fails  immediately        ....  116 
§  3.   Cases  when  bimetallism  fails  after  production  overtakes  con- 
sumption        121 

§  4.   The  limping  standard  ;  the  gold-exchange  standard        .        .  127 

§  5.   Bimetallism  in  France 132 


ANALYTICAL  TABLE  OF  CONTENTS        XIX 

PAGE 

§  6.   Lessons  of  French  experiment 135 

§  7.   The  limping  standard  in  India 138 

§  8.   The  limping  standard  in  the  United  States       ....  140 

§  9.   General  description  of  system  in  the  United  States .        .        .  143 

CHAPTER  VIII 

IwPLtTENCE  OF  Quantity  of  Money  and  Other  Factors  on 
Purchasing  Power  and  on  Each  Other 

§  1.  The  equation  of  exchange  implies  no  causal  sequence  .  .  149 
§  2,   Effects  of  a  change  in  money  (M).     Quantity  theory  in  causal 

sense 151 

§  3.    Quantity  theory  not  strictly  true  during  transition  periods      .  159 

§  4.    Effects  of  a  change  in  deposits  (M')  relatively  to  money  (M)  162 

§  5.    Effects  of  changes  in  velocities  of  circulation  (  V  and  F')        .  164 

§  6.   Effects  of  changes  in  volume  of  trade  (the  §'s)       .         .        .  165 

§  7.  Can  the  price  level  be  regarded  as  cause  as  well  as  effect  ?  .  169 
§  8.   Distinction  between  causation  of  individual  prices  and  the 

price  level 174 

§  9.   Summary 181 

CHAPTEE  IX 

The  Dispersion  of  Prices  makes  necessary  an  Index  OP 
Purchasing  Power 

§  1.   Some  prices  cannot  respond  readily  to  price  movements  .        .  184 

§  2.  Consequently  other  prices  must  over-respond  ....  190 
§  3.    Transformation  of  the  right  side  of  the  equation  of  exchange 

iTom'EpQ  to  PT 194 

§  4.   Summary 196 

CHAPTER  X 

The  Best  Index  Numbers  op  Purchasino  Power 

§  1.  Forms  of  index  numbers 198 

§  2.    Various  purposes  of  index  numbers 204 

§  3.    An  index  number  as  a  standard  of  deferred  payments    .        .  208 

§  4.   Deferred  payments  based  on  total  exchanges  ....  217 

§  5.   Practical  restrictions 225 

§  6.   Summary 231 


XX 


ANALYTICAL  TABLE  OF  CONTENTS 


CHAPTER   XI 
Statistical  Verification.     General  Histobicai.  Review 


§1- 
§2. 
§3. 
§4. 
§5. 
§6. 
§7. 
§8. 
§9. 
§10. 

§11. 
§  12. 
§  13. 
§  14. 
§15. 
§16. 
§17. 
§18. 


§1- 
§2. 
§3. 

§4. 

§5. 

§6. 

§7. 

§8. 

§9. 
§10, 
§11. 


The  last  thousand  years    . 
The  last  four  centuries 
The  nineteenth  century    . 
Its  five  price  movements  . 
Retrospect        .        .        .        , 

Outlook 

Paper  money     .         .        .        . 
Paper  money  in  France    . 
Paper  money  in  England'. 
Paper  money  in  Austria   . 
Early  American  paper  money  . 
The  "  greenbacks  "  . 
Confidence  in  the  greenback     . 
Confederate  paper  money 
Deposit  currency  and  crises 
Particular  crises 
Velocity  of  deposits  and  crises 
Summary 


CHAPTER  Xn 
Statistical  Verification.     Recent  Yeaes 

Professor  Kemmerer's  statistics,  1879-1908 

New  estimates  for  M  and  M',  1890-1909 

New  estimates  for  M'V  and  T"',  1896-1909 

New  estimates  for  3IV  and  T^  1896-1909 

Estimates  for  T  and  P,  1896-1909    , 

P  directly  and  indirectly  calculated 

Correcting  discrepancies   .... 

The  final  results        ..... 

The  comparative  importance  of  price-raising  causes 

Influence  of  antecedent  causes  such  as  tariffs,  etc. 

Results  and  by-products  of  Chapter  XII . 


PAQX 

234 

237 

238 
240 
246 
248 
250 
252 
253 
255 
256 
258 
261 
263 
265 
267 
270 
274 


276 
280 
282 
285 
290 
292 
298 
304 
307 
311 
315 


CHAPTER   XIII 
The  Problem  of  making  Purchasing  Power  more  Stable 

§  1.   The  problem  of  monetary  reform 319 

§  2.    Bimetallism  as  a  solution 323 

§  3.    Other  proposed  solutions 328 

§  4.    The  tabular  standard 332 

§  5.   The  writer's  proposal        ........  337 

§  6.   Summary  and  conclusion 348 


APPENDICES 


Appendix  to  Chapter  II 

FAec 
§  1  (to  Ch.  II,  §  3).  The  concept  of  an  average  ....  349 
§  2  (to  Ch.  11,  §  6).  The  concept  of  velocity  of  circulation  .  .  362 
§  3  (to  Ch.  II,  §  6).  "Arrays"  ofp's,  Q's,  a,ndpQ's  .  .  .355 
§  4  (to  Ch.  II,  §  5).  "  Arrays  "  of  e's,  m's,  and  F's  .  .  .358 
§  5  (to  Ch.  II,  §  5).     The  coin-transfer  concept  of  velocity  and  the 

concept  of  time  of  turnovei 362 

§  6  (to  Ch.  II,  §  6).    Algebraic  demonstration  of  equation  of  ex- 
change          364 

§  7  (to  Ch.  II,  §  6).     P  must  be  a  specific  form  of  average  in  order 

to  vary  directly  as  M  and  V  and  inversely  as  the  §'s,  .        .    364 

Appendix  to  Chapter  III 

§  1  (to  Ch.  in,  §  2).     "  Arrays  "  of  A;'s  and  r's       .        .        .        .367 
§  2  (to  Ch.  in,  §  4).     Algebraic  demonstration  of  equation  of  ex- 
change including  deposit  currency 368 

Appendix  to  Chapter  V 
§  1  (to  Ch.  V,  §  5).    Effect  of  time  credit  on  equation  of  exchange     370 

Appendix  to  Chapter  VI 

§  1  (to  Ch.  VI,  §  1) .    Modification  of  equation  of  exchange  required 

by  international  trade 372 

Appendix  to  Chapter  Vn 

§  1  (to  Ch.  VII,  §  2) .    Money  substitutes  unlike  other  substitutes  .    376 
§  2  (to  Ch.  VII,  §  2).     Limits  for  ratios  within  which  bimetallism 

is  possible 378 

Appendix  to  Chapter  VHI 

§  1  (to  Ch.  VIII,  §  6).     Statistics  of  turnover  at  Yale  University    .     379 
§  2  (to  Ch.  VIII,  §  8).     Four  types  of  commodities  contrasted         .    382 

xxi 


XXll  APPENDICES 


Appendix  to  Chapter  X 


§  1.  Each  form  of  index  number  for  prices  implies  a  correlative 

index  number  for  quantities 385 

§  2.  Index  numbers  for  prices  occur  in  arithmetical  pairs  as  also 
do  index  numbers  for  quantities  .... 

§  3.   General  meanings  of  p's  and  §'s 

§  4.    Review  of  44  formulae,  heading  table  columns 

§  5.    Review  of  8  tests,  heading  table  rows 

§  6.    The  interior  of  the  table  ;  column  11  in  particular 

§  7.   The  44  formulae  compared         .... 

§  8.   Reasons  for  preferring  the  median  practically 

§  9.  Summary 


390 
392 
393 
400 
408 
418 
425 
428 


Appendix  to  Chapter  XII 

§  1  (to  Ch.  Xn,  §  1).  Professor  Kemmerer's  calculations  .  .  430 
§  2  (to  Ch.  XII,  §  2) .  Method  of  calculating  M  .  .  .  .432 
§  3  (to  Ch.  XII,  §  2).  Method  of  calculating  J/'  .  .  .  .434 
§  4  (to  Ch.  XII,  §  3).     Method  of  calculating  M'V  for  1896  and 

1909 441 

§  5  (to  Ch.  XII,  §  3).  Method  of  calculating  MV  for  1897-1908  446 
§  6  (to  Ch.  XII,  §  4).  General  practical  formula  for  calculating  V  448 
§  7  (to  Ch.  XII,  §  4).     Application  of  formula  to  calculations  of 

F  for  1896  and  1909 460 

§  8  (to  Ch.  XII,  §  4).     Interpolating  Values  of  Ffor  1897-1908     .     477 
§  9  (to  Ch.  XII,  §  5).     Method  of  calculating  T     .        .        .        .478 
§  10  (to  Ch.  xn,  §  5).     Method  of  calculating  P     .        .        .        .486 
§  11  (to  Ch.  XII,  §  7).     Mutual  adjustments  of  calculated  values 

oi  M,  M,  V,  W,  P,  T 488 

§  12  (to  Ch.  XII,  §  8).     Credit  and  cash  transactions.     Comparison 

with  Kinley's  estimates 491 

§  13  (to  whole  Ch.).     Addendum  to  second  edition         .        .        .     492 
Appendix  on  "  Standardizing  the  Dollar." 494 


ADDENDUM 

(In  this  revised  edition  figures  for  1910-1912  are  given  on  pages  304,  317. 
See  also  page  492.) 

Data  have  just  become  available  by  which  to  bring  down 
through  1910  the  statistics  of  Chapter  XII.  The  results 
are  as  follows : 


Magnitudes  in  the  Equation  of  Exchange  for  1910* 


M 

M' 

V 

V 

P 

T 

MV+M'V 

PT 

As  first  calculated 

1.64 

7.24 

21 

52.8 

103.7 

397 

416 

412 

As  finally  adjusted 

1.64 

7.23 

21 

52.7 

104.0 

399 

415 

415 

The  table  shows  that  the  figures,  as  first  calculated, 
conform  admirably  to  the  equation  of  exchange.  The 
adjustment  needed,  to  produce  perfect  conformity,  in  only 
one  case  reaches  the  half  of  one  per  cent ! 

From  the  adjusted  figures  we  may  calculate  the  per- 
centages of  cash  and  check  transactions  (^MV-i-  MV ■\-  M'  V 
and  M'V  -i-MV^M'V'~).  These  are  8%  and  92%, 
which  may  be  added  to  the  table  on  page  317.  The 
ratio  of  deposits  to  money  (^M'/M^  is  4.4,  which  shows 

*  The  above  figures  may  be  inserted  by  the  reader  in  the  tables  on 
pages  280,  281,  284,  285,  290,  292,  293,  304.  The  methods  of  deriving 
the  figures  are  in  general  the  same  as  those  explained  in  the  Appendix  to 
Chapter  XII.  The  antecedent  figures  on  which  the  above  table  depends 
may  be  inserted  by  the  reader  as  foUovys  : 

M.  On  page  432  add  (to  the  bottom  of  columns  1-8  incl. )  in  the  table 
the  following :  1910,  3.42,  3.42,  .32,  1.41,  3.3%,  1.46,  1.G4. 

M'.  It  is  not  necessary  to  complete  the  table  on  page  435,  as  the 
Comptroller's  Report  for  1910  (p.  64)  gives  for  the  first  time  deposits 
subject  to  check  (7.82  billions).  To  this  7.82,  however,  three  corrections 
are  needed  :  (1)  subtract  .29  for  "  savings  accounts  "  improperly  included 
(estimated  for  me  by  the  Comptroller's  Office  at  half  of  the  figure  in  note 
a,  lower  table,  p.  64,  Comptr.  Rpt.)  ;  (2)  subtract  .54  as  "exchanges 
for  clearing  house"  (=  f  times  those  for  national  banks)  ;   (3)  add  .25 

xxiii 


XXIV  ADDENDUM 

a  great  increase  over  1909.  The  disproportionate  growth 
of  deposits  relatively  to  money  and  the  excessive  velocity 
of  circulation  (52.7)  of  deposits,  substantially  equal  to  the 
unprecedented  figure  for  1909,  are  disquieting  symptoms 
and  serve  only  to  confirm  the  forebodings  in  the  text. 

For  aid  in  working  out  the  figures  in  this  addendum  I 
am  indebted  to  three  of  my  students,  Mr.  H.  A.  W. 
Duckert,  Mr.  J.  M.  Shortliffe,  and  Mr.  M.  G.  Hastings. 

as  the  Comptroller's  Office  estimate,  for  me,  of  unreported  deposits  sub- 
ject to  check.    By  applying  these  corrections  we  obtain  7.24. 

V.  I  have  simply  taken  21  as  a  safe  approximate  estimate  on  the  basis 
of  the  previous  statistics  of  V  (p.  478)  and  its  assumed  relation  to  V'. 

M'  V  and  V.  Add  to  columns  1-7  of  table  on  page  448  the  following : 
1910,  97.3,  66.4,  429.3,  .89  (by  extrapolation,  an  unsafe  guide),  382,  52.8. 

P.  This  is  obtained  (on  the  principles  of  the  table  on  page  487)  from 
the  index  number  131.6  of  wholesale  prices  for  1910  (kindly  supplied  in 
advance  of  publication  by  the  Bureau  of  Labor)  and  the  average  price 
96.2  of  stocks  as  given  by  the  Commercial  and  Financial  Chronicle,  both 
being  compared  with  the  respective  figures  for  1909,  viz.  126.5  and  97.5. 
They  are  combined  by  "  weighting  "  the  wholesale  prices  10  and  the  stock 
prices  1  and  reducing  the  results  so  that  the  average  for  1909  shall  be  100. 

T.  This  is  obtained :  (a)  by  continuing  columns  1-5  of  the  table  on 
page  479  by  inserting :  1910,  160,  113,  162,  154  ;  (the  extension  of  column 
2  for  1910  is  made  by  means  of  somewhat  more  complete  data  than 
those  enumerated  on  pages  480-482)  ;  (ft)  by  combining  the  result,  154, 
obtained  for  column  5  with  the  figures  for  railway  cars  handled.  These 
were  19.8  millions  for  1909  and  22.3  for  1910.  Column  5  being  weighted 
10  and  the  car  figures  1,  we  get  as  indices  of  trade  :  for  1909,  1718,  and 
for  1910,  1763,  showing  an  increase  of  2.6%,  which,  applied  to  the 
(corrected)  estimate  of  the  absolute  trade  of  1909,  viz.  387  billions,  gives 
397  as  the  absolute  trade  in  1910. 

(The  opportunity  is  here  taken  to  correct  an  inadvertence  on  pp.  480  ff. 
It  should  have  been  there  stated  that,  of  the  44  categories  mentioned, 
some  are  alternative  and  not  independent  items,  viz.  those  having  the 
same  names  and  differing  only  in  the  number  of  cities  ;  also  that  the  dates 
given  do  not  imply  that  the  items  opposite  are  in  all  cases  used  for  all 
the  intervening  time,  but  only  for  such  periods  as  the  items  were  actually 
available.) 

It  is  noticeable  that  the  changes  in  business  in  1910  as  compared  with 
1909  are  somewhat  irregular  ;  the  sales  of  stocks  have  declined ;  exports 
and  imports  (both  of  them)  have  declined  about  10  %. 


THE  PURCHASING  POWER  OF  MONEY 


THE  PUECHASING  POWER  OF  MONEY 


CHAPTER  II 

PRIMARY   DEFINITIONS 


In  order  to  make  clear  the  relation  which  the  topic 
treated  in  this  book  bears  to  the  general  subject  of 
economics,    some    primary    definitions    are   necessary. 

In  the  first  place,  economics  itself  may  be  defined  as 
the  science  of  wealth,  and  wealth  may  be  defined  as 
material  objects  owned  by  human  beings.  Of  wealth, 
therefore,  there  are  two  essential  attributes :  material- 
ity and  appropriation.  For  it  is  not  all  material  things 
that  are  included  under  wealth,  but  only  such  as  have 
been  appropriated.  Wealth  does  not  include  the  sun, 
moon,  and  other  heavenly  bodies,  nor  even  all  parts 
of  the  surface  of  this  planet,  but  only  such  parts  as 
have  been  appropriated  to  the  use  of  mankind.  It 
is,  then,  appropriated  parts  of  the  earth's  surface  and 
the  appropriated  objects  upon  it  which  constitute 
wealth. 

For  convenience,  wealth  may  be  classified  under 
three  heads :  real  estate,  commodities,  and  human 
beings.  Real  estate  includes  the  surface  of  the  earth 
and  the  other  wealth  attached  thereto  —  improvements 
such  as  buildings,  fences,  drains,  railways,  street  im- 

'  This  chapter  is  mainly  a  condensation  of  Chapters  I  and  II  of 
the  author's  Nature  of  Capital  and  Income,  New  York  (Macmillan), 
1906. 

B  1 


2  THE    PURCHASING   POWER   OF  MONEY        [Chap.  I 

provements,  and  so  on.  Commodities  include  all  mova- 
ble wealth  (except  man  himself),  whether  raw  materials 
or  finished  products.  There  is  one  particular  variety 
of  commodity  —  a  certain  finished  product  — ■  which 
is  of  especial  importance  in  the  subject  of  which  this 
book  treats ;  namely,  money.  Any  commodity  to  be 
called  "  money  "  must  be  generally  acceptable  in  exchange, 
and  any  commodity  generally  acceptable  in  exchange 
should  be  called  money.  The  best  example  of  a  money 
commodity  is  found  to-day  in  gold  coins. 

Of  all  wealth,  man  himself  is  a  species.  Like  his 
horses  or  his  cattle,  he  is  himself  a  material  object,  and 
like  them,  he  is  owned ;  for  if  slave,  he  is  owned  by 
another,  and  if  free,  by  himself.^ 

But  though  human  beings  may  be  considered  as 
wealth,  human  qualities,  such  as  skill,  intelligence,  and 
inventiveness,  are  not  wealth.  Just  as  the  hardness 
of  steel  is  not  wealth,  but  merely  a  quality  of  one  par- 
ticular kind  of  wealth,  —  hard  steel,  —  so  the  skill  of  a 
workman  is  not  wealth,  but  merely  a  quality  of  another 
particular  kind  of  wealth  —  skilled  workman.  Similarly, 
intelligence  is  not  wealth,  but  an  intelhgent  man  is 
wealth. 

Since  materiality  is  one  of  the  two  essential  attributes 
of  wealth,  any  article  of  wealth  may  be  measured  in 
physical  units.  Land  is  measured  in  acres ;  coal,  in 
tons  ;  milk,  in  quarts ;  and  wheat,  in  bushels.  There- 
fore, for  estimating  the  quantities  of  different  articles 
of  wealth,  all  the  various  physical  units  of  measurement 

*  If  we  wish  to  include  only  slaves  as  wealth  and  not  free  men, 
we  shall  have  to  amend  our  definition  of  wealth  so  as  to  read : 
Wealth  consists  of  material  objects  owned  by  human  beings  and 
external  to  the  owner.  For  the  purpose  of  this  book  it  makes  no 
practical  difference  whether  this  narrower  meaning  or  the  broader 
one  be  employed. 


Sec.  1]  PRIMARY   DEFINITIONS  3 

may  be  employed :  linear  measure,  square  measure, 
cubic  measure,  and  measure  by  weight. 

Whenever  any  species  of  wealth  is  measured  in  its 
physical  units,  a  first  step  is  taken  toward  the  measure- 
ment of  that  mysterious  magnitude  called  ''value." 
Sometimes  value  is  looked  upon  as  a  psychical  and  some- 
times as  a  physical  phenomenon.  But,  although  the 
determination  of  value  always  involves  a  psychical 
process  —  judgment  —  yet  the  terms  in  which  the  re- 
sults are  expressed  and  measured  are  physical. 

It  is  desirable,  for  the  sake  of  clearness,  to  lead  up 
to  the  concept  of  value  by  means  of  three  preliminary 
concepts  ;  namely,  transfer,  exchange,  and  price. 

A  transfer  of  wealth  is  a  change  in  its  ownership. 
An  exchange  consists  of  two  mutual  and  voluntary 
transfers,  each  in  consideration  of  the  other. 

When  a  certain  quantity  of  one  kind  of  wealth  is 
exchanged  for  a  certain  quantity  of  another  kind,  we 
may  divide  one  of  the  two  quantities  by  the  other, 
and  obtain  the  price  of  the  latter.  For  instance,  if 
two  dollars  of  gold  are  exchanged  for  three  bushels  of 
wheat,  the  price  of  the  wheat  in  gold  is  two  thirds  of  a 
dollar  per  bushel ;  and  the  price  of  the  gold  in  wheat 
is  one  and  a  half  bushels  per  dollar.  It  is  to  be  noticed 
that  these  are  ratios  of  two  physical  quantities,  the  units 
for  measuring  which  are  quite  different  from  each  other. 
One  commodity  is  measured  in  bushels,  or  units  of 
volume  of  wheat,  the  other  in  dollars,  or  units  of  weight 
of  gold.  In  general,  a  price  of  any  species  of  wealth  is 
merely  the  ratio  of  two  physical  quantities,  in  whatever 
way  each  may  originally  be  measured. 

This  brings  us,  at  last,  to  the  concept  of  value.  The 
value  of  any  item  of  wealth  is  its  price  multiplied  by  its 
quantity.     Thus,  if  half  a  dollar  per  bushel  is  the  price 


4  THE    PURCHASING    POWER   OF   MONEY        [Chap.  1 

of  wheat,  the  value  of  a  hundred  bushels  of  wheat  is 
fifty  dollars. 

§2 

Hitherto  we  have  confined  our  discussion  to  some 
of  the  consequences  of  the  first  prerequisite  of  wealth  — 
that  it  must  be  material.  We  turn  now  to  the  second 
prerequisite,  namely,  that  it  must  be  owned.  To  own 
wealth  is  simply  to  have  the  right  to  benefit  by  it 
that  is,  the  right  to  enjoy  its  services  or  benefits.  Thus 
the  owner  of  a  loaf  of  bread  has  the  right  to  benefit  bj 
it  by  eating  it,  by  selling  it,  or  by  otherwise  disposing 
of  it.  The  man  who  owns  a  house  has  the  right  to 
benefit  by  enjoying  its  shelter,  by  selling  it,  or  by  rent- 
ing it.  This  right,  the  right  to  or  in  the  benefits  of 
wealth — or  more  briefly,  the  right  to  or  in  the  wealth  it- 
self — •  is  called  a  "  property  right "  or  simply  "property." 

If  things  were  always  owned  in  fee  simple,  i.e.  if  there 
were  no  division  of  ownership, — no  partnership  rights, 
no  shares,  and  no  stock  companies,  —  there  would  be 
little  practical  need  to  distinguish  property  from  wealth ; 
and  as  a  matter  of  fact,  in  the  rough  popular  usage,  any 
article  of  wealth,  and  especially  real  estate,  is  often 
inaccurately  called  a  "piece  of  property."  But  the 
ownership  of  wealth  is  frequently  divided;  and  this 
fact  necessitates  a  careful  distinction  between  the  thing 
owned  and  the  rights  of  the  owners.  Thus,  a  railroad 
is  wealth.  Its  shares  and  bonded  debt  are  rights  to 
this  wealth.  Each  owner  of  shares  or  bonds  has  the 
right  to  a  fractional  part  of  the  benefits  from  the  railway. 
The  total  of  these  rights  comprises  the  complete  owner- 
ship of,  or  property  in,  the  railway. 

Like  wealth,  property  rights  also  may  be  meas- 
ured ;  but  in  units  of  a  different  character.     The  units 


Sec.  2]  PRIMARY  DEFINITIONS  5 

of  property  are  not  physical,  but  consist  of  abstract 
rights  to  the  benefits  of  wealth.  If  a  man  has  twenty- 
five  shares  in  a  certain  railway  company,  the  measure- 
ment of  his  property  is  twenty-five  units  just  as  truly 
as  though  he  had  twenty-five  bushels  of  wheat.  What 
he  has  is  twenty-five  rights  of  a  specific  sort. 

There  exist  various  units  of  property  for  measuring 
property,  as  there  are  various  units  of  wealth  for  meas- 
uring wealth ;  and  to  property  may  be  applied  pre- 
cisely the  same  concepts  of  transfer,  exchange,  price, 
and  value  which  are  applied  to  wealth. 

Besides  the  distinction  between  wealth  and  property 
rights,  another  distinction  should  here  be  noted.  This  is 
the  distinction  between  property  rights  and  certificates 
of  those  rights.  The  former  are  the  rights  to  use  wealth, 
the  latter  are  merely  the  written  evidence  of  those  rights. 
Thus,  the  right  to  receive  dividends  from  a  railroad 
is  property,  but  the  writjten  paper  evidencing  that 
right  is  a  stock  certificate.  TT!&^%jh.t  to  a  railway 
trip  is  a  property  right,  the  ticket  evidencing  that 
right  is  a  certificate  of  property.  The  promise  of 
a  bank  is  a  property  right ;  the  bank  note  on 
which  that  promise  is  engraved  is  a  certificate  of 
property. 

Any  property  right  which  is  generally  acceptable  in 
exchange  may  be  called  "money."  Its  printed  evi- 
dence is  also  called  money.  Hence  there  arise  three 
meanings  of  the  term  money,  viz.  its  meaning  in  the 
sense  of  wealth  ;  its  meaning  in  the  sense  of  property ;  ^ 
and  its  meaning  in  the  sense  of  written  evidence. 
From  the  standpoint  of  economic  analysis  the  prop- 
erty sense  is  the  most  important. 

^  Cf.  Menger,  Handworterbuch  der  Siaatswissenschaften,  Jena 
(Fischer),  Vol.  IV,  1900,  Article,  "Geld,"  pp.  69-71. 


6  THE   PURCHASING   POWER  OP  MONEY       [Chap.  I 

What  we  have  been  speaking  of  as  property  is  the  right 
to  the  services,  uses,  or  benefits  of  wealth.  By  benefits 
of  wealth  is  meant  the  desirable  events  which  occur  by 
means  of  wealth.  Like  wealth  and  property,  benefits 
also  may  be  measured,  but  in  units  of  a  still  different 
character.  Benefits  are  reckoned  either ' '  by  time, "  —  as 
the  services  of  a  gardener  or  of  a  dwelling  house;  or 
"by  the  piece,"  —  as  the  use  of  a  plow  or  a  telephone. 
And  just  as  the  concepts  of  transfer,  exchange,  price, 
and  value  apply  to  wealth  and  property,  so  do  they 
apply  to  benefits. 

The  uses  (benefits)  of  wealth,  with  which  we  have  been 

\4ealing,   should  be  distinguished  from  the  utility  of 

wealth.    The  one  means  desirable  events,  the  other, 

the  desirability  of  those  events.     The  one  is  usually 

outside  of  the  mind,  the  other  always  inside. 

Whenever  we  speak  of  rights  to  benefits,  the  benefits 
referred  to  are  future  benefits.  The  owner  of  a  house 
owns  the  right  to  use  it  from  the  present  instant  on- 
ward. Its  past  use  has  perished  and  is  no  longer  sub- 
ject to  ownership. 

The  term  "goods"  will  be  used  in  this  book  simply  as 
a  convenient  collective  term  to  include  wealth,  property, 
and  benefits.  The  transfer,  exchange,  price,  and  value  of 
goods  take  on  innumerable  forms.  Under  price  alone, 
as  thus  fully  applied  to  goods,  fall  rent,  wages,  rates 
of  interest,  prices  in  terms  of  money,  and  prices  in 
terms  of  other  goqds.  But  we  shall  be  chiefly  con- 
cerned in  this  book  with  prices  of  goods  in  terms  of 
money. 

§3 

Little  has  yet  been  said  as  to  the  relation  of  wealth, 
property  and  benefits  to  time.  A  certain  quantity 
of  goods  may  be  either  a  quantity  existing  at  a  partic- 


Sec.  3]  PRIMARY   DEFINITIONS  7 

ular  instant  of  time  or  a  quantity  produced,  consumed, 
transported,  or  exchanged  during  a  period  of  time. 
The  first  quantity  is  a  stock,  or  fund,  of  goods ;  the 
second  is  a  flow,  or  stream,  of  goods.  The  amount  of 
wheat  in  a  flour  mill  on  any  definite  date  is  a  stock  of 
wheat,  while  the  monthly  or  weekly  amounts  which 
come  in  or  go  out  constitute  a  flow  of  wheat.  The 
amount  of  mined  coal  existing  in  the  United  States  at 
any  given  moment  is  a  stock  of  mined  coal ;  the  weekly 
amount  mined  is  a  flow  of  coal. 

There  are  many  applications  of  this  distinction ;  for 
instance,  to  capital  and  income.  A  stock  of  goods, 
whether  wealth  or  property,  existing  at  an  instant  of 
time  is  called  capital.  A  flow  of  benefits  from  such 
capital  during  a  period  of  time  is  called  "  income."  In- 
come, therefore,  is  one  important  kind  of  economic  flow. 
Besides  income,  economic  flows  are  of  three  chief  classes, 
representing  respectively  changes  of  condition  (such 
as  production  or  consumption),  changes  of  position  (such 
as  transportation,  exportation,  and  importation),  and 
changes  of  ownership,  which  we  have  already  called 
"  transfers."  Trade  is  a  flow  of  transfers.  Whether  for- 
eign or  domestic,  it  is  simply  the  exchange  of  a  stream  of 
transferred  rights  in  goods  for  an  equivalent  stream 
of  transferred  money  or  money  substitutes.  The  second 
of  these  two  streams  is  called  the  "circulation"  of  money. 
The  equation  between  the  two  is  called  the  "equation 
of  exchange  " ;  and  it  is  this  equation  that  constitutes 
the  subject  matter  of  the  present  book. 


CHAPTER  II 

PURCHASING  POWER  OF  MONEY  AS  RELATED  TO  THE 
EQUATION  OF  EXCHANGE 

§  1 

We  define  money  as  what  is  generally  acceptable  in 
exchange  for  goods. ^  The  facility  with  which  it  may 
thus  be  exchanged,  or  its  general  acceptability,  is  its 
distinguishing  characteristic.  The  general  acceptability 
may  be  reenforced  by  law,  the  money  thus  becoming 
what  is  known  as  "legal  tender";  but  such  reenforce- 
ment  is  not  essential.  All  that  is  necessary  in  order  that 
any  good  may  be  money  is  that  general  acceptability 
attach  to  it.  On  the  frontier,  without  any  legal  sanc- 
tion, money  is  sometimes  gold  dust  or  gold  nuggets. 
In  the  Colony  of  Virginia  it  was  tobacco.  Among  the 
Indians  in  New  England  it  was  wampum.  "In  German 
New  Guinea  the  bent  tusks  of  a  boar  are  used  as  money. 
In  Cahfornia  red  birds'  heads  have  been  used  in  the 
same  way."  ^  Stone  money  and  shell  money  are  so  used 
in  Melanesia.^  "In  Burmah  Chinese  gambling  counters 
are  used  as   money.     Guttapercha   tokens  issued  by 

1  For  discussions  on  the  definition  of  money,  see  A.  Piatt  An- 
drew, "What  ought  to  be  called  Money"  in  Quarterly  Journal  of 
Economics,  Vol.  XIII ;  Jevons,  Money  and  the  Mechanism  of  Ex- 
change, London  (Kegan  Paul)  and  New  York  (Appleton),  1896; 
Palgrave,  Dictionary  of  Political  Economy;  Walker,  Money,  and 
other  treatises  and  textbooks. 

2  Sumner,  Folkways,  Boston  (Ginn),  1907,  p.  147. 

3  Ibid.,  p.  150. 

8 


Sec.  1]  THE   EQUATION    OF  EXCHANGE  9 

street  car  companies  in  South  America  are  said  to  be 
used  in  the  same  way."  ^  Not  many  years  ago  in  a 
town  in  New  York  state,  similar  tokens  got  into  local 
circulation  until  their  issue  was  forbidden  by  the  United 
States  government.  In  Mexico  large  cacao  beans 
of  relatively  poor  quahty  were  used  as  money,  and  on 
the  west  coast  of  Africa  little  mats  were  used.^  The 
list  could  be  extended  indefinitely.  But  whatever  the 
substance  of  such  a  commodity,  it  is  general  exchange- 
ability which  makes  it  money. 

On  the  other  hand,  even  what  is  made  legal  tender 
may,  by  general  usage,  be  deprived  of  its  practical  char- 
acter as  money.  During  the  Civil  War  the  govern- 
ment attempted  to  circulate  fifty-dollar  notes,  bearing 
interest  at  7.3  per  cent,  so  that  the  interest  amounted 
to  the  very  easily  computed  amount  of  a  cent  a  day. 
The  notes,  however,  failed  to  circulate.  In  spite  of  the 
attempt  to  make  their  exchange  easy,  people  preferred 
to  keep  them  for  the  sake  of  the  interest.^  Money 
never  bears  interest  except  in  the  sense  of  creating  con- 
venience in  the  process  of  exchange.  This  convenience 
is  the  special  service  of  money  and  offsets  the  apparent 
loss  of  interest  involved  in  keeping  it  in  one's  pocket 
instead  of  investing. 

There  are  various  degrees  of  exchangeability  which 
must  be  transcended  before  we  arrive  at  real  money. 
Of  all  kinds  of  goods,  perhaps  the  least  exchangeable 
is  real  estate.  Only  in  case  some  person  happens  to  be 
found  who  wants  it,  can  a  piece  of  real  estate  be  traded. 
A  mortgage  on  real  estate  is  one  degree  more  exchange- 
able. Yet  even  a  mortgage  is  less  exchangeable  than  a 
well-known  and  safe  corporation  security ;   and  a  cor- 

1  Sumner,  Folkways,  p.  148.  '^  Ibid. 

'  See  Jevons,  Money  and  the  Mechanism  of  Exchange,  p.  245. 


10  THE   PURCHASING   POWER   OF  MONEY      [Chap.  II 

poration  security  is  less  exchangeable  than  a  government 
bond.  In  fact  persons  not  infrequently  buy  govern- 
ment bonds  as  merely  temporary  investments,  intending 
to  sell  them  again  as  soon  as  permanent  investments 
yielding  better  interest  are  obtainable.  One  degree 
more  exchangeable  than  a  government  bond  is  a  bill 
of  exchange ;  one  degree  more  exchangeable  than  a  bill 
of  exchange  is  a  sight  draft ;  while  a  check  is  almost 
as  exchangeable  as  money  itself.  Yet  no  one  of  these 
is  really  money  for  none  of  them  is  ^^  generally  accept- 
able." 

If  we  confine  our  attention  to  present  and  normal 
conditions,  and  to  those  means  of  exchange  which  either 
are  money  or  most  nearly  approximate  it,  we  shall 
find  that  money  itself  belongs  to  a  general  class  of 
property  rights  which  we  may  call  "  currency "  or 
'^ circulating  media."  Currency  includes  any  type  of 
property  right  which,  whether  generally  acceptable  or 
not,  does  actually,  for  its  chief  purpose  and  use,  serve 
as  a  means  of  exchange. 

Circulating  media  are  of  two  chief  classes  :  (1)  money ; 
(2)  bank  deposits,  which  will  be  treated  fully  in  the  next 
chapter.  By  means  of  checks,  bank  deposits  serve  as 
a  means  of  payment  in  exchange  for  other  goods.  A 
check  is  the  "certificate"  or  evidence  of  the  transfer 
of  bank  deposits.  It  is  acceptable  to  the  payee  only 
by  his  consent.  It  would  not  be  generally  accepted  by 
strangers.  Yet  by  checks,  bank  deposits  even  more 
than  money  do  actually  serve  as  a  medium  of  exchange. 
Practically  speaking,  money  and  bank  deposits  subject 
to  check  are  the  only  circulating  media.  If  post-office 
orders  and  telegraphic  transfer  are  to  be  included,  they 
may  be  regarded  as  certificates  of  transfer  of  special 
deposits,  the  post  oflfice  or  telegraph  company  serving 


Sec.  1]  THE   EQUATION   OF  EXCHANGE  11 

the  purpose,  for  these  special  transactions,  of  a  bank  of 
deposit. 

But  while  a  bank  deposit  transferable  by  check  is 
included  as  circulating  media,  it  is  not  money.  A 
bank  note,  on  the  other  hand,  is  both  circulating 
medium  and  money.  Between  these  two  lies  the  final 
line  of  distinction  between  what  is  money  and  what 
is  not.  True,  the  line  is  delicately  drawn,  especially 
when  we  come  to  such  checks  as  cashier's  checks  or 
certified  checks,  for  the  latter  are  almost  identical  with 
bank  notes.  Each  is  a  demand  liability  on  a  bank, 
and  each  confers  on  the  holder  the  right  to  draw  money. 
Yet  while  a  note  is  generally  acceptable  in  exchange,  a 
check  is  specially  acceptable  only,  i.e.  only  by  the  con- 
sent of  the  payee.  Real  money  rights  are  what  a  payee 
accepts  without  question,  because  he  is  induced  to  do 
so  either  by  ''legal  tender"  laws  or  by  a  well-established 
custom.^ 

Of  real  money  there  are  two  kinds :  primary  and 
fiduciary.  Money  is  called  "  primary"  if  it  is  a  commod- 
ity which  has  just  as  much  value  in  some  use  other  than 
money  as  it  has  in  monetary  use.  Primary  money  has 
its  full  value  independently  of  any  other  wealth.  Fidu- 
ciary money,  on  the  other  hand,  is  money  the  value 
of  which  depends  partly  or  wholly  on  the  confidence 
that  the  owner  can  exchange  it  for  other  goods,  e.g.  for 
primary  money  at  a  bank  or  government  office,  or  at  any 
rate  for  discharge  of  debts  or  purchase  of  goods  of  mer- 
chants. The  chief  example  of  primary  money  is  gold 
coin ;  the  chief  example  of  fiduciary  money  is  bank 
notes.  The  qualities  of  primary  money  which  make  for 
exchangeability  are  numerous.     The  most  important 

*  See  Francis  Walker,  Money,  Trade,  and  Industry,  New  York 
(Holt),  1879,  Chapter  I. 


12  THE   PURCHASING   POWER   OF  MONEY      [Chap.  II 

are  portability,  durability,  and  divisibility.^  The  chief 
quality  of  fiduciary  money  which  makes  it  exchangeable 
is  its  redeemability  in  primary  money,  or  else  its  im- 
posed character  of  legal  tender. 

Bank  notes  and  all  other  fiduciary  money,  as  well  as 
bank  deposits,  circulate  by  certificates  often  called 
''tokens."  ''Token  coins"  are  included  in  this  de- 
scription. The  value  of  these  tokens,  apart  from  the 
rights  they  convey,  is  small.  Thus  the  value  of  a  silver 
dollar,  as  wealth,  is  only  about  forty  cents ;  that  is  all 
that  the  actual  silver  in  it  is  worth.  Its  value  as  prop- 
erty, however,  is  one  hundred  cents ;  for  its  holder  has 
a  legal  right  to  use  it  in  paying  a  debt  to  that  amount, 
and  a  customary  right  to  so  use  it  in  payment  for 
goods.  Likewise,  the  property  value  of  a  fifty-cent 
piece,  a  quarter,  a  ten-cent  piece,  a  five-cent  piece,  or 
a  one-cent  piece  is  considerably  greater  than  its  value 
as  wealth.  The  value  of  a  paper  dollar  as  wealth  —  for 
instance,  a  silver  certificate  —  is  almost  nothing.  It  is 
worth  just  its  value  as  paper,  and  no  more.  But  its 
value  as  property  is  a  hundred  cents,  that  is,  the  equiva- 
lent of  one  gold  dollar.  It  represents  to  that  extent  a 
claim  of  the  holder  on  the  wealth  of  the  community. 

Figure  1  indicates  the  classification  of  all  circulating 
media  in  the  United  States.  It  shows  that  the  total 
amount  of  circulating  media  is  about  8|  billions,  of 
which  about  7  billions  are  bank  deposits  subject  to 
check,  and  1^  billions,  money ;  and  that  of  this  1^ 
billions  of  money,  1  billion  is  fiduciary  money  and  only 
about  I  a  billion,  primary  money. 

In  the  present  chapter  we  shall  exclude  the  consider- 
ation of  bank  deposits  or  check  circulation  and  confine 
our  attention  to   the  circulation  of   money,   primary 

1  See  Jevons,  Money  and  the  Mechanism  of  Exchange,  Chapter  V. 


Sec.  1] 


THE   EQUATION    OF   EXCHANGE 


13 


and  fiduciary.  In  the  United  States,  the  only  primary 
money  is  gold  coin.  The  fiduciary  money  includes 
(1)  token  coins,  viz.  silver  dollars,  fractional  silver, 
and  minor  coins  ("nickels"  and  cents);  (2)  paper 
money,  viz.  (a)  certifi- 


Deposits  subject 

TO  CHECK 


Fiduciary 

MONEY 


MOWEY 
BlLUION 


Billions 


Fig.  1. 


cates  for  gold  and  sil- 
ver, and  (6)  promissory 
notes,  whether  of  the 
United  States  govern- 
ment ("greenbacks"), 
or  of  the  National 
banks. 

Checks  aside,  we 
may  classify  exchanges 
into  three  groups :  the 

/'exchange  of  goods 
against  goods,  or  bar- 
ter;   the    exchange  of 

.  money  against  money,  or  changing  money;  and  the 
\5'  exchange  of  money  against  goods,  or  purchase  and  sale. 
Only  the  last-named  species  of  exchange  makes  up  what 
we  call  the  "circulation"  of  money.  The  circulation 
of  money  signifies,  therefore,  the  aggregate  amount  of 
its  transfers  against  goods.  All  money  held  for  circula- 
tion, i.e.  all  money,  except  what  is  in  the  banks  and 
United  States  government's  vaults,  is  called  "money  in 
circulation." 

The  chief  object  of  this  book  is  to  explain  the  causes 
determining  the  purchasing  power  of  money.  The 
purchasing  power  of  money  is  indicated  by  the  quan- 
tities of  other  goods  which  a  given  quantity  of  money 
will  buy.  The  lower  we  find  the  prices  of  goods,  the 
larger  the  quantities  that  can  be  bought  by  a  given 
amount  of  money,  and  therefore  the  higher  the  purchas- 


14  THE    PURCHASING    POWER   OF  MONEY      [Chap.  II 

ing  power  of  money.  The  higher  we  find  the  prices 
of  goods,  the  smaller  the  quantities  that  can  be  bought 
by  a  given  amount  of  money,  and  therefore  the  lower 
the  purchasing  power  of  money.  In  short,  the  purchas- 
ing power  of  money  is  the  reciprocal  of  the  level  of 
prices ;  so  that  the  study  of  the  purchasing  power  of 
money  is  identical  with  the  study  of  price  levels. 

§2 

Overlooking  the  influence  of  deposit  currency,  or 
checks,  the  price  level  may  be  said  to  depend  on  only 
three  sets  of  causes  :  (1)  the  quantity  of  money  in  circu- 
lation ;  (2)  its  "efficiency"  or  velocity  of  circulation  (or 
the  average  number  of  times  a  year  money  is  exchanged 
for  goods) ;  and  (3)  the  volume  of  trade  (or  amount  of 
goods  bought  by  money).  The  so-called  "quantity 
theory,"  ^  i.e.  that  prices  vary  proportionately  to  money, 
has  often  been  incorrectly  formulated,  but  (overlooking 
checks)  the  theory  is  correct  in  the  sense  that  the  level 
of  prices  varies  directly  with  the  quantity  of  money  in 
circulation,  provided  the  velocity  of  circulation  of  that 
money  and  the  volume  of  trade  which  it  is  obliged  to 
perform  are  not  changed. 

The  quantity  theory  has  been  one  of  the  most  bitterly 
contested  theories  in  economics,  largely  because  the 
recognition  of  its  truth  or  falsity  affected  powerful 

^  This  theory,  though  often  crudely  formulated,  has  been  accepted 
by  Locke,  Hume,  Adam  Smith,  Ricardo,  Mill,  Walker,  IMarshall, 
Hadley,  Fetter,  Kemmerer  and  most  writers  on  the  subject.  The 
Roman  Julius  Paulus,  about  200  a.d.,  stated  his  belief  that  the 
value  of  money  depends  on  its  quantity.  See  Zuckerkandl,  Theorie 
des  Preises;  Kemmerer,  Money  and  Credit  Instruments  in  their 
Relation  to  General  Prices,  New  York  (Holt),  1909.  It  is  true 
that  many  writers  still  oppose  the  quantity  theory.  See  especially, 
Laughlin,  Principles  of  Money,  New  York  (Scribner),  1903. 


Sec.  2]  THE   EQUATION   OF  EXCHANGE  15 

interests  in  commerce  and  politics.  It  has  been  main- 
tained —  and  the  assertion  is  scarcely  an  exaggeration 
—  that  the  theorems  of  Euclid  would  be  bitterly  con- 
troverted if  financial  or  political  interests  were  in- 
volved. 

The  quantity  theory  has,  unfortunately,  been  made 
the  basis  of  arguments  for  unsound  currency  schemes. 
It  has  been  invoked  in  behalf  of  irredeemable  paper 
money  and  of  national  free  coinage  of  silver  at  the  ratio 
of  16  to  1.  As  a  consequence,  not  a  few  ''sound  money 
men,"  believing  that  a  theory  used  to  support  such 
vagaries  must  be  wrong,  and  fearing  the  political  effects 
of  its  propagation,  have  drifted  into  the  position  of 
opposing,  not  only  the  unsound  propaganda,  but  also 
the  sound  principles  by  which  its  advocates  sought 
to  bolster  it  up.^  These  attacks  upon  the  quantity 
theory  have  been  rendered  easy  by  the  imperfect  com- 
prehension of  it  on  the  part  of  those  who  have  thus 
invoked  it  in  a  bad  cause. 

Personally,  I  believe  that  few  mental  attitudes  are 
more  pernicious,  and  in  the  end  more  disastrous,  than 
those  which  would  uphold  sound  practice  by  denying 
sound  principles  because  some  thinkers  make  unsound 
application  of  those  principles.  At  any  rate,  in  scien- 
tific study  there  is  no  choice  but  to  find  and  state  the 
liji varnished  truth. 

The  quantity  theory  will  be  made  more  clear  by  the 
equation  of  exchange,  which  is  now  to  be  explained. 

The  equation  of  exchange  is  a  statement,  in  math- 

*  See  Scott,  "It  has  been  a  most  fruitful  source  of  false  doctrines 
regarding  monetary  matters,  and  is  constantly  and  successfully 
employed  in  defense  of  harmful  legislation  and  as  a  means  of  pre- 
venting needed  monetary  reforms."  Money  and  Banking,  New 
York,  1903,  p.  68. 


16  THE    PURCHASING    POWER   OF  MONEY      [Chap.  II 

ematical  form,  of  the  total  transactions  effected  in  a 
certain  period  in  a  given  community.  It  is  obtained 
simply  by  adding  together  the  equations  of  exchange  for 
all  individual  transactions.  Suppose,  for  instance,  that 
a  person  buys  10  pounds  of  sugar  at  7  cents  per  pound. 
This  is  an  exchange  transaction,  in  which  10  pounds  of 
sugar  have  been  regarded  as  equal  to  70  cents,  and  this 
fact  may  be  expressed  thus :  70  cents  =  10  pounds  of 
sugar  multiplied  by  7  cents  a  pound.  Every  other  sale 
and  purchase  may  be  expressed  similarly,  and  by  adding 
them  all  together  we  get  the  equation  of  exchange  for 
a  certain  -period  in  a  given  community.  During  this 
same  period,  however,  the  same  money  may  serve, 
and  usually  does  serve,  for  several  transactions.  For 
that  reason  the  money  side  of  the  equation  is  of 
course  greater  than  the  total  amount  of  money  in  cir- 
culation. 

The  equation  of  exchange  relates  to  all  the  purchases 
made  by  money  in  a  certain  community  during  a  cer- 
tain time.  We  shall  continue  to  ignore  checks  or  any 
circulating  medium  not  money.  We  shall  also  ignore 
foreign  trade  and  thus  restrict  ourselves  to  trade  within 
a  hypothetical  community.  Later  we  shall  reinclude 
these  factors,  proceeding  by  a  series  of  approximations 
through  successive  hypothetical  conditions  to  the  actual 
conditions  which  prevail  to-day.  We  must,  of  course, 
not  forget  that  the  conclusions  expressed  in  each  suc- 
cessive approximation  are  true  solely  on  the  particular 
hypothesis  assumed. 

The  equation  of  exchange  is  simply  the  sum  of  the 
equations  involved  in  all  individual  exchanges  in  a  year. 
In  each  sale  and  purchase,  the  money  and  goods  ex- 
changed are  ipso  facto  equivalent ;  for  instance,  the 
money  paid  for  sugar  is  equivalent  to  the  sugar  bought. 


Sec.  2]  THE   EQUATION   OF   EXCHANGE  17 

And  in  the  grand  total  of  all  exchanges  for  a  year,  the 
total  money  paid  is  equal  in  value  to  the  total  value 
of  the  goods  bought.  The  equation  thus  has  a  money 
side  and  a  goods  side.  The  money  side  is  the  total 
money  paid,  and  may  be  considered  as  the  product  of  y 
the  quantity  of  money  multiplied  by  its  rapidity  of 
circulation.  The  goods  side  is  made  up  of  the  products 
of  quantities  of  goods  exchanged  multiplied  by  their 
respective  prices. 

The  important  magnitude,  called  the  velocity  of  cir- 
culation, or  rapidity  of  turnover,  is  simply  the  quotient  y^ 
obtained  by  dividing  the  total  money  payments  for  • 
goods  in  the  course  of  a  year  by  the  average  amount 
of  money  in  circulation  by  which  those  payments  are 
effected.  This  velocity  of  circulation  for  an  entire  com- 
munity is  a  sort  of  average  of  the  rates  of  turnover  of 
money  for  different  persons.  Each  person  has  his  own 
rate  of  turnover  which  he  can  readily  calculate  by  di- 
viding the  amount  of  money  he  expends  per  year  by 
the  average  amount  he  carries. 

•  Let  us  begin  with  the  money  side.  If  the  number  of 
dollars  in  a  country  is  5,000,000,  and  their  velocity  of 
circulation  is  twenty  times  per  year,  then  the  total 
amount  of  money  changing  hands  (for  goods)  per  year 
is  5,000,000  times  twenty,  or  $100,000,000.  This  is  the 
money  side  of  the  equation  of  exchange. 

Since  the  money  side  of  the  equation  is  $100,000,000, 
the  goods  side  must  be  the  same.  For  if  $100,000,000 
has  been  spent  for  goods  in  the  course  of  the  year,  then 
$100,000,000  worth  of  goods  must  have  been  sold  in 
that  year.  In  order  to  avoid  the  necessity  of  writing 
out  the  quantities  and  prices  of  the  innumerable  va- 
rieties of  goods  which  are  actually  exchanged,  let  us 
assume  for  the  present  that  there  are  only  three  kinds 


18  THE    PURCHASING    POWER   OF   MONEY      [Chap.  U 

of  goods,  —  bread,  coal,  and  cloth  ;   and  that  the  sales 

are:  — 

200,000,000  loaves  of  bread  at  $  .10  a  loaf, 
10,000,000  tons  of  coal  at  5.00  a  ton,  and 

30,000,000  yards  of  cloth  at       1 .00  a  yard. 

The  value  of  these  transactions  is  evidently  $100,000,- 
000,  i.e.  $20,000,000  worth  of  bread  plus  $50,000,000 
worth  of  coal  plus  $30,000,000  worth  of  cloth.  The 
equation  of  exchange  therefore  (remember  that  the 
money  side  consisted  of  $5,000,000  exchanged  20  times) 
is  as  follows  :  — 

S5,000,000  X  20  times  a  year 

=  200,000,000  loaves  X  $  .10  a  loaf 
+    10,000,000  tons     X    5.00  a  ton 
+   30,000,000  yards   X    1.00  a  yard. 

This  equation  contains  on  the  money  side  two  magni- 
tudes, viz.  (1)  the  quantity  of  money  and  (2)  its 
velocity  of  circulation ;  and  on  the  goods  side  two 
groups  of  magnitudes  in  two  columns,  viz.  (1)  the 
quantities  of  goods  exchanged  (loaves,  tons,  yards), 
and  (2)  the  prices  of  these  goods.  The  equation  shows 
that  these  four  sets  of  magnitudes  are  mutually  related. 
Because  this  equation  must  be  fulfilled,  the  prices  must 
bear  a  relation  to  the  three  other  sets  of  magnitudes,  — 
quantity  of  money,  rapidity  of  circulation,  and  quan- 
tities of  goods  exchanged.  Consequently,  these  prices 
must,  as  a  whole,  vary  proportionally  with  the  quantity 
of  money  and  with  its  velocity  of  circulation,  and  in- 
versely with  the  quantities  of  goods  exchanged. 

Suppose,  for  instance,  that  the  quantity  of  money 
were  doubled,  while  its  velocity  of  circulation  and  the 
quantities  of  goods  exchanged  remained  the  same. 
Then  it  would  be  quite  impossible  for  prices  to 
remain  unchanged.    The  money  side  would  now  be 


Sec.  2]  THE   EQUATION   OF  EXCHANGE  19 

$10,000,000  X  20  times  a  year  or  $200,000,000  ;  whereas, 
if  prices  should  not  change,  the  goods  would  remain 
$100,000,000,  and  the  equation  would  be  violated. 
Since  exchanges,  individually  and  collectively,  always 
involve  an  equivalent  quid  pro  quo,  the  two  sides  must 
be  equal.  Not  only  must  purchases  and  sales  be  equal 
in  amount  —  since  every  article  bought  by  one  person 
is  necessarily  sold  by  another  —  but  the  total  value  of 
goods  sold  must  equal  the  total  amount  of  money 
exchanged.  Therefore,  under  the  given  conditions, 
prices  must  change  in  such  a  way  as  to  raise  the  goods 
side  from  $100,000,000  to  $200,000,000.  This  doubling 
may  be  accomplished  by  an  even  or  uneven  rise  in 
prices,  but  some  sort  of  a  rise  of  prices  there  must  he. 
If  the  prices  rise  evenly,  they  will  evidently  all  be  exactly 
doubled,  so  that  the  equation  will  read  :  — 

$10,000,000  X  20  times  a  year 

=  200,000,000  loaves  X  $  .20  per  loaf 
+  10,000,000  tons  X  10.00  per  ton 
+   30,000,000  yards   X      2.00  per  yard. 

If  the  prices  rise  unevenly,  the  doubling  must  evidently 
be  brought  about  by  compensation ;  if  some  prices  rise 
by  less  than  double,  others  must  rise  by  enough  more 
than  double  to  exactly  compensate. 

But  whether  all  prices  increase  uniformly,  each  being 
exactly  doubled,  or  some  prices  increase  more  and  some 
less  (so  as  still  to  double  the  total  money  value  of  the 
goods  purchased),  the  prices  are  doubled  on  the  average} 
This  proposition  is  usually  expressed  by  saying  that  the 
"general  level  of  prices"  is  raised  twofold.  From  the 
mere  fact,  therefore,  that  the  money  spent  for  goods 

1  This  does  not  mean,  of  course,  that  their  simple  arithmetical 
average  is  exactly  doubled.  For  definition  of  an  average  or  "mean" 
in  general,  see  §  1  of  Appendix  to  (this)  Chapter  II. 


20  THE    PURCHASING    POWER   OF   MONEY      [Chap.  II 

must  equal  the  quantities  of  those  goods  multipHed  by 
their  prices,  it  follows  that  the  level  of  prices  must  rise 
or  fall  according  to  changes  in  the  quantity  of  money, 
unless  there  are  changes  in  its  velocity  of  circulation  or 
in  the  quantities  of  goods  exchanged. 

If  changes  in  the  quantity  of  money  affect  prices,  so 
will  changes  in  the  other  factors  —  quantities  of  goods 
and  velocity  of  circulation  —  affect  prices,  and  in  a 
very  similar  manner.  Thus  a  doubling  in  the  velocity 
of  circulation  of  money  will  double  the  lev«l  of  prices, 
provided  the  quantity  of  money  in  circulation  and  the 
quantities  of  goods  exchanged  for  money  remain  as  be- 
fore.    The  equation  will  become :  — 

$5,000,000  X  40  times  a  year 

=  200,000,000  loaves  X  $  .20  a  loaf 
+  10,000,000  tons  X  10.00  a  ton 
+   30,000,000  yards   X      2.00  a  yard, 

or  else  the  equation  will  assume  a  form  in  which  some 
of  the  prices  will  more  than  double,  and  others  less  than 
double  by  enough  to  preserve  the  same  total  value  of 
the  sales. 

Again,  a  doubling  in  the  quantities  of  goods  exchanged 
will  not  double,  but  halve,  the  height  of  the  price  level, 
provided  the  quantity  of  money  and  its  velocity  of 
circulation  remain  the  same.  jJnder  these  circum- 
stances the  equation  will  become :  — 


),000,000  X  20  times  a  year 


=  400,000,000  loaves  X  S  .05  a  loaf 
+  20,000,000  tons  X  2.50  a  ton 
+    60,000,000  yards   X     .50  a  yard, 


or  else  it  will  assume  a  form  in  which  some  of  the  prices 
are  more  than  halved,  and  others  less  than  halved, 
BO  as  to  preserve  the  equation. 


Sec.  3] 


THE    EQUATION   OF   EXCHANGE 


21 


Finally,  if  there  is  a  simultaneous  change  in  two  or 
all  of  the  three  influences,  i.e.  quantity  of  money, 
velocity  of  circulation,  and  quantities  of  goods  ex- 
changed, the  price  level  will  be  a  compound  or  resultant 
of  these  various  influences.  If,  for  example,  the  quan- 
tity of  money  is  doubled,  and  its  velocity  of  circulation 
is  halved,  while  the  quantity  of  goods  exchanged  remains 
constant,  the  price  level  will  be  undisturbed.  Like- 
wise, it  will  be  undisturbed  if  the  quantity  of  money  is 
doubled  an^  the  quantity  of  goods  is  doubled,  while 
the  velocity  of  circulation  remains  the  same.  To  double 
the  quantity  of  money,  therefore,  is  not  always  to  double 
prices.  We  must  distinctly  recognize  that  the  quantity 
of  money  is  only  one  of  three  factors,  all  equally  impor- 
tant in  determining  the  price  level. 


§3 

The  equation  of  exchange  has  now  been  expressed  by 
an  arithmetical  illustration.  It  may  be  also  represented 
visually,  by  a  mechanical  illustration.  Such  a  repre- 
sentation is  embodied  in  Figure  2.     This  represents  a 


Fig.  2. 


mechanical  balance  in  equilibrium,  the  two  sides  of  which 
symbolize  respectively  the  money  side  and  the  goods 
side  of  the  equation  of  exchange.  The  weight  at  the 
left,  symbolized  by  a  purse,  represents  the  money  in 
circulation;  the  ''arm"  or  distance  from  the  fulcrum 
at  which  this  weight  (purse)  is  hung  represents  the 


22  THE    PURCHASING    POWER   OF   MONEY      [Chap.  II 

efficiency  of  this  money,  or  its  velocity  of  circulation. 
On  the  right  side  are  three  weights,  —  bread,  coal,  and 
cloth,  symbolized  respectively  by  a  loaf,  a  coal  scuttle, 
and  a  roll  of  cloth.  The  arm,  or  distance  of  each  from 
the  fulcrum,  represents  its  price.  In  order  that  the  lever 
arms  at  the  right  may  not  be  inordinately  long,  we  have 
found  it  convenient  to  reduce  the  unit  of  measure  of 
coal  from  tons  to  hundredweights,  and  that  of  cloth 
from  yards  to  feet,  and  consequently  to  enlarge  corre- 
spondingly the  numbers  of  units  (the  measure  of  coal 
changing  from  10,000,000  tons  to  200,000,000  hundred- 
weights, and  that  of  the  cloth  from  30,000,000  yards  to 
90,000,000  feet).  The  price  of  coal  in  the  new  unit  per 
hundredweight  becomes  25  cents  per  hundredweight, 
and  that  of  cloth  in  feet  becomes  SS-g-  cents  per  foot. 

We  all  know  that,  when  a  balance  is  in  equilibrium, 
the  tendency  to  turn  in  one  direction  equals  the  tend- 
ency to  turn  in  the  other.  Each  weight  produces  on 
its  side  a  tendency  to  turn,  measured  by  the  product  of 
the  weight  by  its  arm.  The  weight  on  the  left  produces, 
on  that  side,  a  tendency  measured  by  5,000,000  x  20; 
while  the  weights  on  the  right  make  a  combined  opposite 
tendency  measured  by  200,000,000  x  .10  +  200,000,000  x 
.25-^90,000,000  X  ..33i  The  equality  of  these  opposite 
tendencies  represents  the  equation  of  exchange. 

An  increase  in  the  weights  or  arms  on  one  side  re- 
quires, in  order  to  preserve  equilibrium,  a  proportional 
increase  in  the  weights  or  arms  on  the  other  side.  This 
simple  and  familiar  principle,  applied  to  the  symbolism 
here  adopted,  means  that  if,  for  instance,  the  velocity 
of  circulation  (left  arm)  remains  the  same,  and  if  the 
trade  (weights  at  the  right)  remains  the  same,  then  any 
increase  of  the  purse  at  the  left  will  require  a  lengthen- 
ing of  one  or  more  of  the  arms  at  the  right,  represent- 


Sec.  3] 


THE   EQUATION   OF   EXCHANGE 


23 


ing  prices.  If  these  prices  increase  uniformly,  they  will 
increase  in  the  same  ratio  as  the  increase  in  money ;  if 
they  do  not  increase  uniformly,  some  will  increase  more 
and  some  less  than  this  ratio,  maintaining  an  average. 

Likewise  it  is  evident  that  if  the  arm  at  the  left 
lengthens,  and  if  the  purse  and  the  various  weights  on 
the  right  remain  the  same,  there  must  be  an  increase  in 
the  arms  at  the  right. 

Again,  if  there  is  an  increase  in  weights  at  the  right, 
and  if  the  left  arm  and  the  purse  remain  the  same,  there 
must  be  a  shortening  of  right  arms. 

In  general,  a  change  in  one  of  the  four  sets  of  mag- 
nitudes must  be  accompanied  by  such  a  change  or 
changes  in  one  or  more  of  the  other  three  as  shall  main- 
tain equilibrium. 

As  we  are  interested  in  the  average  change  in  prices 
rather  than  in  the  prices  individually,  we  may  simplify 
this  mechanical  representation  by  hanging  all  the  right- 
hand  weights  at  one  average  point,  so  that  the  arm  shall 
represent  the  average  prices.  This  arm  is  a  ''weighted 
average"  of  the  three  original  arms,  the  weights  being 
literally  the  weights  hanging  at  the  right. 

This  averaging  of  prices  is  represented  in  Figure  3, 
which  visualizes  the  fact  that  the  average  price  of  goods 


X__Mi 


Pro 


(right  arm)  varies  directly  with  the  quantity  of  money 
(left  weight),  and  directly  with  its  velocity  of  circulation 


24  THE    PURCHASING   POWER   OF  MONEY      [Chap.  II 

(left  arm),  and  inversely  with  the  volume  of  trade  (right 
weight). 

§4 

We  now  come  to  the  strict  algebraic  statement  of 
the  equation  of  exchange.  An  algebraic  statement  is 
usually  a  good  safeguard  against  loose  reasoning  ; 
and  loose  reasoning  is  chiefly  responsible  for  the  sus- 
picion under  which  economic  theories  have  frequently 
fallen.  If  it  is  worth  while  in  geometry  to  demonstrate 
carefully,  at  the  start,  propositions  which  are  almost 
self-evident,  it  is  a  hundredfold  more  worth  while  to 
demonstrate  with  care  the  propositions  relating  to 
price  levels,  which  are  less  self-evident ;  which,  indeed, 
while  confidently  assumed  by  many,  are  contemptuously 
rejected  by  others. 

Let  us  denote  the  total  circulation  of  money,  i.e.  the 
amount  of  money  expended  for  goods  in  a  given  com- 
munity during  a  given  year,  by  E  (expenditure) ;  and 
the  average  amount  of  money  in  circulation  in  the  com- 
munity during  the  year  by  M  (money).  M  will  be 
the  simple  arithmetical  average  of  the  amounts  of  money 
existing  at  successive  instants  separated  from  each 
other  by  equal  intervals  of  time  indefinitely  small. 
If  we  divide  the  year's  expenditures,  E,  by  the  average 
amount  of  money,  M,  we  shall  obtain  what  is  called 
the  average  rate  of  turnover  of  money  in  its  exchange 

E 

for  goods,  — ,  that  is,  the  velocity  of   circulation  of 

money.  ^    This  velocity  may  be  denoted  by  V,  so  that 

E 

/    ijj  =  ^J    then    E   may    be    expressed    as    MV.      In 

words :   the  total  circulation  of  money  in  the  sense  of 

^  For  discussion  of  the  concept  of  velocity  of  circulation,  see 
§§  2,  4,  5  of  Appendix  to  (this)  Chapter  II. 


Sec.  4]  THE    EQUATION   OF   EXCHANGE  25 

money  expended  is  equal  to  the  total  money  in  circu- 
lation multiplied  by  its  velocity  of  circulation  or  turn- 
over. E  ovMV,  therefore,  expresses  the  money  side  of 
the  equation  of  exchange.  Turning  to  the  goods  side 
of  the  equation,  we  have  to  deal  with  the  prices  of 
goods  exchanged  and  quantities  of  goods  exchanged. 
The  average^  price  of  sale  of  any  particular  good, 
such  as  bread,  purchased  in  the  given  community 
during  the  given  year,  may  be  represented  by  p 
(price) ;  and  the  total  quantity  of  it  purchased,  by  Q 
(quantity) ;  hkewise  the  average  price  of  another 
good  (say  coal)  may  be  represented  by  p'  and  the 
total  quantity  of  it  exchanged,  by  Q' ;  the  average 
price  and  the  total  quantity  of  a  third  good  (say  cloth) 
may  be  represented  by  p"  and  Q"  respectively ;  and  so 
on,  for  all  other  goods  exchanged,  however  numerous. 
The  equation  of  exchange  may  evidently  be  expressed 
as  follows :  ^  — 

MV  =  pQ 

+  v'Q' 

+  P"Q" 

+  etc. 

^  This  is  an  average  weighted  according  to  the  quantities  pur- 
chased on  various  occasions  throughout  the  period  and  country 
considered.     See  §  3  of  Appendix  to  (this)  Chapter  II. 

2  An  algebraic  statement  of  the  equation  of  exchange  was  made 
by  Simon  Newcomb  in  his  able  but  little  appreciated  Principles 
of  Political  Economy,  New  York  (Harper),  1885,  p.  346.  It  is  also 
expressed  by  Edgeworth,  "  Report  on  Monetary  Standard."  Report 
of  the  British  Association  for  the  Advancement  of  Science,  1887,  p. 
293,  and  by  President  Hadley,  Economics,  New  York  (Putnam), 
1896,  p.  197.  See  also  Irving  Fisher,  "The  Role  of  Capital  in  Eco- 
nomic Theory,"  Economic  Journal,  December,  1899,  pp.  515-521, 
and  E.  W.  Kemmerer,  Money  and  Credit  Instruments  in  their  Rela- 
tion to  General  Prices,  New  York  (Holt),  1907,  p.  13.  While  thus 
only  recently  given  mathematical  expression,  the  quantity  theory 
has  long  been  understood  as  a  relationship  among  the  several  fac- 


26  THE    PURCHASING   POWER   OF  MONEY      [Chap.  II 

The  right-hand  side  of  this  equation  is  the  sum  of 

terms  of  the  form  pQ  —  a  price  multipHed  by  a  quantity 

bought.     It  is  customary  in  mathematics  to  abbreviate 

such  a  sum  of  terms  (all  of  which  are  of  the  same  form) 

by  using  ''2  "  as  a  symbol  of  summation.     This  symbol 

does  not  signify  a  magnitude  as  do  the  symbols  Af ,  V, 

p,  Q,  etc.     It  signifies  merely  the  operation  of  addition 

and  should  be  read  ''the  sum  of  terms  of  the  following 

type."     The  equation   of  exchange  may  therefore  be 

written :  — 

MV  =  SpQ. 

That  is,  the  magnitudes  E,  M,  V,  the  p's  and  the  Q's 
relate  to  the  entire  community  and  an  entire  year ;  but 
they  are  based  on  and  related  to  corresponding  magni- 
tudes for  the  individual  persons  of  which  the  community 
is  composed  and  for  the  individual  moments  of  time 
of  which  the  year  is  composed.^ 

The  algebraic  derivation  of  this  equation  is,  of  course, 
essentially  the  same  as  the  arithmetical  derivation 
previously  given.  It  consists  simply  in  adding  together 
the  equations  for  all  individual  purchases  within  the 
community  during  the  year.- 

By  means  of  this  equation,  MV  =  ^pQ,  the  three 
theorems  set  forth  earlier  in  this  chapter  may  be  now 
expressed  as  follows  :  — 

(1)  If  V  and  the  Q's  remain  invariable  while  M  varies 
in  any  ratio,  the  money  side  of  the  equation  will  vary 

tors :  amount  of  money,  rapidity  of  circulation,  and  amount  of  trade. 
See  Mill,  Principles  of  Political  Economy,  Book  III,  Chapter  VIII, 
§  3.    Ricardo  probably  deserves  chief  credit  for  launching  the  theory. 

"  For  the  relations  subsisting  between  these  magnitudes  (as 
relating  to  the  whole  community  and  the  whole  year),  and  the 
corresponding  elementary  magnitudes  relating  to  each  individual 
and  each  moment,  see  §  4  of  the  Appendix  to  (this)  Chapter  II. 

^  See  §  6  of  Appendix  to  (this)  Chapter  II. 


Sec.  4]  THE   EQUATION   OF  EXCHANGE  27 

in  the  same  ratio  and  therefore  its  equal,  the  goods  side, 
must  vary  in  that  same  ratio  also ;  consequently,  either 
the  p's  will  all  vary  in  that  ratio  or  else  some  p's  will 
vary  more  than  in  that  ratio  and  others  enough  less  to 
compensate  and  maintain  the  same  average.^ 

(2)  If  M  and  the  Q's  remain  invariable  while  V  varies 
in  any  ratio,  the  money  side  of  the  equation  will  vary 
in  the  same  ratio,  and  therefore  its  equal,  the  goods 
side,  must  vary  in  that  ratio  also;  consequently,  the 
p's  will  all  vary  in  the  same  ratio  or  else  some  will  vary 
more  and  others  enough  less  to  compensate. 

(3)  If  Af  and  V  remain  invariable,  the  money  side 
and  the  goods  side  will  remain  invariable ;  consequently, 
if  the  Q's  all  vary  in  a  given  ratio,  either  the  p's  must 
all  vary  in  the  inverse  ratio  or  else  some  of  them  will 
vary   more   and   others   enough   less   to   compensate. 

We  may,  if  we  wish,  further  simplify  the  right  side 
by  writing  it  in  the  form  PT  where  P  is  a  weighted 
average  of  all  the  p's,  and  T  is  the  sum  of  all  the  Q's. 
P  then  represents  in  one  magnitude  the  level  of  prices, 
and  T  represents  in  one  magnitude  the  volume  of  trade. 
This  simplification  is  the  algebraic  interpretation  of 
the  mechanical  illustration  given  in  Figure  3,  where  all 
the  goods,  instead  of  being  hung  separately,  as  in 
Figure  2,  were  combined  and  hung  at  an  average  point 
representing  their  average  price. 

We  have  derived  the  equation  of  exchange,  MV  = 
^vQ,  by  adding  together,  for  the  right  side,  the  sums 
expended  by  different  persons.  But  the  same  reasoning 
would  have  derived  an  equation  of  exchange  by  taking 
the  sums  received  by  different  persons.    The  results  of 

'  For  the  nature  of  the  average  here  involved  and  for  the  aver- 
ages involved  in  the  other  two  following  cases,  see  §  7  of  Appendix 
to  (this)  Chapter  II. 


1/ 


28  THE    PURCHASING   POWER   OF  MONEY      [Chap.  II 

the  two  methods  will  harmonize  if  the  community  has 
no  foreign  trade ;  for,  apart  from  foreign  trade,  what  is 
expended  by  one  person  in  the  community  is  necessarily 
received  by  some  other  person  in  that  community. 

If  we  wish  to  extend  the  reasoning  so  as  to  apply 
to  foreign  trade,  we  shall  have  two  equations  of  ex- 
change, one  based  on  money  expended  and  the  other 
on  money  received  or  accepted  by  members  of  the  com- 
munity. These  will  always  be  approximately  equal  and 
may  or  may  not  be  exactly  equal  within  a  country  ac- 
cording to  the  "balance  of  trade"  between  that  coun- 
try and  others.  The  right  side  of  the  equation  based 
on  expenditures  will  include,  in  addition  to  the  domes- 
tic quantities  already  represented  there,  the  quantities 
of  goods  imporlsd  and  their  prices,  but  not  those  ex- 
ported;  whilo  the  reverse  will  be  true  of  the  equation 
based  on  receipts. 

§5 

This  completes  our  statement  of  the  equation  of 
exchange,  except  for  the  element  of  check  payments, 
which  is  reserved  for  the  next  chapter.  We  have  seen 
that  the  equation  of  exchange  has  as  its  ultimate  basis 
the  elementary  equations  of  exchange  pertaining  to  given 
persons  and  given  moments,  in  other  words,  the  equa- 
tions pertaining  to  individual  transactions.  Such  ele- 
mentary equations  mean  that  the  money  paid  in  any 
transaction  is  the  equivalent  of  the  goods  bought  at 
the  price  of  sale.  From  this  secure  and  obvious  premise 
is  derived  the  equation  of  exchange  MV  =  '^pQ,  each 
element  in  which  is  a  sum  or  an  average  of  the  like 
elementary  elements  for  different  individuals  and  differ- 
ent moments,  thus  comprising  all  the  purchases  in  the 
community  during  the  year.     Finally,  from  this  equa- 


Sec.  5]  THE   EQUATIOJS    OF  EXCHANGE  29 

tion  we  see  that  prices  vary  directly  as  M  and  F,  and 
inversely  as  the  Q's,  provided  in  each  case  only  one  of 
these  three  sets  of  magnitudes  varies,  and  the  other  two 
remain  unchanged.  Whether  to  change  one  of  the 
three  necessarily  disturbs  the  others  is  a  question  re- 
served for  a  later  chapter.  Those  who  object  to  the 
equation  of  exchange  as  a  mere  truism  are  asked  to 
defer  judgment  until  they  have  read  Chapter  VIII. 

To  recapitulate,  we  find  then  that,  under  the  con- 
ditions assumed,  the  price  level  varies  (1)  directly  as  the 
quantity  of  money  in  circulation  (M),  (2)  directly  as 
the  velocity;  of  its  circulation  (F),  (3)  inversely  as  the 
volume  of  trade  done  by  it  (T).  The  first  of  these 
three  relations  is  worth  emphasis.  It  constitutes  the 
"  quantity  theory  of  money." 

So  important  is  this  principle,  and  so  bitterly  con- 
tested has  it  been,  that  we  shall  illustrate  it  further. 
As  already  indicated,  by  "the  quantity  of  money"  is 
meant  the  number  of  dollars  (or  other  given  monetary 
units)  in  circulation.  This  number  may  be  changed 
in  several  ways,  of  which  the  following  three  are  most 
important.  Their  statement  will  serve  to  bring  home 
to  us  the  conclusions  we  have  reached  and  to  reveal  the 
fundamental  peculiarity  of  money  on  which  they  rest. 

As  a  first  illustration,  let  us  suppose  the  government 
to  double  the  denominations  of  all  money ;  that  is,  let 
us  suppose  that  what  has  been  hitherto  a  half  dollar  is 
henceforth  called  a  dollar,  and  that  what  has  hitherto 
been  a  dollar  is  henceforth  called  two  dollars.  Evi- 
dently the  number  of  "dollars"  in  circulation  will  then 
be  doubled ;  and  the  price  level,  measured  in  terms 
of  the  new  "dollars,"  will  be  double  what  it  would 
otherwise  be.  Every  one  will  pay  out  the  same  coins 
as  though  no  such  law  were  passed.     But  he  will,  in 


30  THE   PURCHASING   POWER   OF  MONEY      [Chap.  II 

each  case,  be  paying  twice  as  many  ''dollars."  Fol 
example,  if  $3  formerly  had  to  be  paid  for  a  pair  of 
shoes,  the  price  of  this  same  pair  of  shoes  will  now 
become  $6.  Thus  we  see  how  the  nominal  quantity  of 
money  affects  price  levels. 

A  second  illustration  is  found  in  a  debased  currency. 
Suppose  a  government  cuts  each  dollar  in  two,  coining 
the  halves  into  new  ''dollars" ;  and,  recalling  all  paper 
notes,  replaces  them  with  double  the  original  number  — • 
two  new  notes  for  each  old  one  of  the  same  denomination. 
In  short,  suppose  money  not  only  to  be  renamed,  as  in 
the  first  illustration,  but  also  reissued ;  prices  in  the  de- 
based coinage  will  again  be  doubled  just  as  in  the  first 
illustration.  The  subdivision  and  recoinage  is  an  im- 
material circumstance,  unless  it  be  carried  so  far  as 
to  make  counting  difficult  and  thus  to  interfere  with 
the  convenience  of  money.  Wherever  a  dollar  had 
been  paid  before  debasement,  two  dollars  —  i.e.  two 
of  the  old  halves  coined  into  two  of  the  new  dollars  — 
will  now  be  paid  instead. 

In  the  first  illustration,  the  increase  in  quantity  was 
simply  nominal,  being  brought  about  by  renaming 
coins.  In  the  second  illustration,  besides  renaming,  the 
further  fact  of  recoining  is  introduced.  In  the  first 
case  the  number  of  actual  pieces  of  money  of  each  kind 
was  unchanged,  but  their  denominations  were  doubled. 
In  the  second  case,  the  number  of  pieces  is  also  doubled 
by  splitting  each  coin  and  reminting  it  into  two  coins, 
each  of  the  same  nominal  denomination  as  the  original 
whole  of  which  it  is  the  half,  and  by  similarly  redoubUng 
the  paper  money. 

For  a  third  illustration,  suppose  that,  instead  of 
doubhng  the  number  of  dollars  by  splitting  them  in 
two  and  recoining  the  halves,  the  government  duplicates 


Sec.  5J  THE   EQUATION   OF  EXCHANGE  31 

each  piece  of  money  in  existence  and  presents  the  du- 
phcate  to  the  possessor  of  the  original.^  (We  must  in 
this  case  suppose,  further,  that  there  is  some  effectual 
bar  to  prevent  the  melting  or  exporting  of  money. 
Otherwise  the  quantity  of  money  in  circulation  will 
not  be  doubled :  much  of  the  increase  will  escape.)  If 
the  quantity  of  money  is  thus  doubled,  prices  will  also 
be  doubled  just  as  truly  as  in  the  second  illustration,  in 
which  there  were  exactly  the  same  denominations.  The 
only  difference  between  the  second  and  the  third 
illustrations  will  be  in  the  size  and  weight  of  the  coins. 
The  weights  of  the  individual  coins,  instead  of  being 
reduced,  will  remain  unchanged ;  but  their  number 
will  be  doubled.  This  doubling  of  coins  must  have  the 
same  effect  as  the  50  per  cent  debasement,  i.e.  it  must 
have  the  effect  of  doubling  prices. 

The  force  of  the  third  illustration  becomes  even  more 
evident  if,  in  accordance  with  Ricardo's  presentation,^ 
we  pass  back  by  means  of  a  seigniorage  from  the  third 
illustration  to  the  second.  That  is,  after  duplicating 
all  money,  let  the  government  abstract  half  of  each  coin, 
thereby  reducing  the  weight  to  that  of  the  debased 
coinage  in  the  second  illustration,  and  removing  the 
only  point  of  distinction  between  the  two.  This 
''seigniorage"  abstracted  will  not  affect  the  value  of  the 
coins,   so   long   as   their   number  remains   unchanged. 

In  short,  the  quantity  theory  asserts  that  (provided 
velocity  of  circulation  and  volume  of  trade  are  un- 
changed) if  we  increase  the  number  of  dollars,  whether 

^  Cf.  J.  S.  Mill,  Principles  of  Political  Economy,  Book  III,  Chap- 
ter VIII,  §  2.  Ricardo  in  his  reply  to  Bosanquet  uses  an  illus- 
tration similar  in  principle  though  slightly  different  in  form.  See 
Works,  2d  ed.,  London  (Murray),  1852,  p.  346. 

»  Works,  2d  ed.,  London  (Murray),  1852,  pp.  346  and  347 
(reply  to  Bosanquet,  Chapter  VI) ;   see  also  pp.  213  and  214. 


32  THE   PURCHASING   POWER   OF   MONEY      [Chap.  II 

by  renaming  coins,  or  by  debasing  coins,  or  by  increasing 
coinage,  or  by  any  other  means,  prices  will  be  increased 
in  the  same  proportion.  It  is  the  number,  and  not 
the  weight,  that  is  essential.  This  fact  needs  great 
emphasis.  It  is  a  fact  which  differentiates  money 
from  all  other  goods  and  explains  the  peculiar  manner  in 
which  its  purchasing  power  is  related  to  other  goods. 
Sugar,  for  instance,  has  a  specific  desirability  dependent 
on  its  quantity  in  pounds.  Money  has  no  such  quality. 
The  value  of  sugar  depends  on  its  actual  quantity.  If 
the  quantity  of  sugar  is  changed  from  1,000,000  pounds 
to  1,000,000  hundredweight,  it  does  not  follow  that  a 
hundredweight  will  have  the  value  previously  possessed 
by  a  pound.  But  if  money  in  circulation  is  changed 
from  1,000,000  units  of  one  weight  to  1,000,000  units 
of  another  weight,  the  value  of  each  unit  will  remain 
unchanged. 

The  quantity  theory  of  money  thus  rests,  ultimately, 
upon  the  fundamental  pecuUarity  which  money  alone  of 
all  goods  possesses,  —  the  fact  that  it  has  no  power  to 
satisfy  human  wants  except  a  power  to  purchase  things 
which  do  have  such  power. ^ 

1  Cf .  G.  F.  Knapp,  Staatliche  Theorie  des  Geldes,  Leipzig,  1905 ; 
L.  von  Bortkiewiez,  "  Die  geldtheoretischen  und  die  wahrungspoli- 
tisehen  Consequenzen  des  '  Nominalismus,' "  Jahrbuch  fiir  Gesetz- 
gebung,  Verwaltung  und  Volkswirtschaft,  October,  1906 ;  Bertrand 
Nogaro,  "  L'experience  bimetalliste  du  XIX  siecle  et  la  theorie 
generale  de  la  monnaie,"  Revue  d'Economie  politique,  1908. 


CHAPTER   III 

INFLUENCE   OF   DEPOSIT    CURKENCY    ON    THE    EQUATION 
AND   THEREFORE    ON  PURCHASING   POWER 

§    1 

We  are  now  ready  to  explain  the  nature  of  bank 
deposit  currency,  or  circulating  credit.  Credit,  in 
general,  is  the  claim  of  a  creditor  against  a  debtor. 
Bank  deposits  subject  to  check  are  the  claims  of  the 
creditors  of  a  bank  against  the  bank,  by  virtue  of  which 
they  may,  on  demand,  draw  by  check  specified  sums 
of  money  from  the  bank.  Since  no  other  kind  of  bank 
deposits  will  be  considered  by  us,  we  shall  usually 
refer  to  "bank  deposits  subject  to  check"  simply  as 
''bank  deposits."  They  are  also  called  "circulating 
credit."  Bank  checks,  as  we  have  seen,  are  merely 
certificates  of  rights  to  draw,  i.e.  to  transfer  bank  de- 
posits. The  checks  themselves  are  not  the  currency; 
the  bank  deposits  which  they  represent  are  the  currency. 

It  is  in  the  connection  with  the  transfer  of  bank 
deposits  that  there  arises  that  so-called  "mystery  of 
banking"  called  "circulating  credit."  Many  persons, 
including  some  economists,  have  supposed  that  credit 
is  a  special  form  of  wealth  which  may  be  created 
out  of  whole  cloth,  as  it  were,  by  a  bank.  Others  have 
maintained  that  credit  has  no  foundation  in  actual 
wealth  at  all,  but  is  a  kind  of  unreal  and  inflated  bubble 
with  a  precarious,  if  not  wholly  illegitimate,  existence. 
As  a  matter  of  fact,  bank  deposits  are  as  easy  to  under- 
stand as  bank  notes,  and  what  is  said  in  this  chapter 
D  33 


34  THE    PURCHASING   POWER   OF  MONEY     [Chap.  Ill 

of  bank  deposits  may  in  substance  be  taken  as  true 
also  of  bank  notes.  The  chief  difference  is  a  formal  one, 
the  notes  circulating  from  hand  to  hand,  while  the 
deposit  currency  circulates  only  by  means  of  special 
orders  called  "checks." 

To  understand  the  real  nature  of  bank  deposits,  let 
us  imagine  a  hypothetical  institution,  —  a  kind  of 
primitive  bank  existing  mainly  for  the  sake  of  deposits 
and  the  safe  keeping  of  actual  money.  The  original 
bank  of  Amsterdam  was  somewhat  like  the  bank  we 
are  now  imagining.  In  such  a  bank  a  number  of  people 
deposit  $100,000  in  gold,  each  accepting  a  receipt  for  the 
amount  of  his  deposit.  If  this  bank  should  issue  a 
''capital  account,"  or  statement,  it  would  show  $100,000 
in  its  vaults  and  $100,000  owed  to  depositors,  as  fol- 
lows :  — 

Assets  Liabilities 

Gold $100,000  I  Due  depositors     .     .    $100,000 

The  right-hand  side  of  the  statement  is,  of  course, 
made  up  of  smaller  amounts  owed  to  individual  de- 
positors. Assuming  that  there  is  owed  to  A,  $10,000, 
to  B,  $10,000,  and  to  all  others  $80,000,  we  may  write 
the  bank  statement  as  follows  :  — 

Assets  Liabilities 


Gold $100,000 


$100,000 


Due  depositor  A  .  .  $10,000 
Due  depositor  B  .  .  10,000 
Due  other  depositors        80,000 

$100,000 


Now  assume  that  A  wishes  to  pay  B  $1000.  A  could 
go  to  the  bank  with  B,  present  certificates  or  checks 
for  $1000,  obtain  the  gold,  and  hand  it  over  to  B,  who 
might  then  redeposit  it  in  the  same  bank,  merely  hand- 


Sec.  1]  DEPOSIT   CURRENCY  35 

ing  it  back  through  the  cashier's  window  and  taking  a 
new  certificate  in  his  own  name.  Instead,  however, 
of  both  A  and  B  visiting  the  bank  and  handhng  the 
money,  A  might  simply  give  B  a  check  for  $1000.  The 
transfer  in  either  case  would  mean  that  A's  holding  in 
the  bank  was  reduced  from  S  10,000  to  $9000,  and  that 
B's  was  increased  from  $10,000  to  $11,000.  The  state- 
ment would  then  read  :  — 

Assets  Liabilities 


Gold $100,000 


$100,000 


Due  depositor  A  .  .  $  9,000 
Due  depositor  B  .  .  11,000 
Due  other  depositors         80,000 


$100,000 


Thus  the  certificates,  or  checks,  would  circulate  in 
place  of  cash  among  the  various  depositors  in  the  bank. 
What  really  changes  ownership,  or  ''circulates,"  in 
such  cases  is  the  rigM  to  draw  money.  The  check  is 
merely  the  evidence  of  this  right  and  of  the  transfer  of 
ohis  right  from  one  person  to  another. 

In  the  case  under  consideration,  the  bank  would  be  con- 
ducted at  a  loss.  It  would  be  giving  the  time  and  labor 
of  its  clerical  force  for  the  accommodation  of  its  deposi- 
tors, without  getting  anything  in  return.  But  such  a 
hypothetical  bank  would  soon  find  —  much  as  did  the 
bank  of  Amsterdam^  —  that  it  could  ''make  money"  by 
lending  at  interest  some  of  the  gold  on  deposit.  This 
could  not  offend  the  depositors;  for  they  do  not  expect 
or  desire  to  get  back  the  identical  gold  they  de- 
posited. What  they  want  is  simply  to  be  able  at  any 
time  to  obtain  the  same  amount  of  gold.     Since,  then, 

1  See  Dunbar's  Theory  and  History  of  Banking,  2d  ed.,  edited 
by  O.  M.  W.  Sprague,  New  York  and  London  (G.  P.  Putnam's 
Sons),  1901,  pp.  113-116. 


36 


THE   PURCHASING   POWER   OF  MONEY     [Chap.  Ill 


their  arrangement  with  the  bank  calls  for  the  payment^ 
not  of  any  particular  gold,  but  merely  of  a  definite 
amount,  and  that  but  occasionally,  the  bank  finds  it- 
self free  to  lend  out  part  of  the  gold  that  otherwise 
would  lie  idle  in  its  vaults.  To  keep  it  idle  would  be 
a  great  and  needless  waste  of  opportunity. 

Let  us  suppose,  then,  that  the  bank  decides  to  loan 
out  half  its  cash.  This  is  usually  done  in  exchange  for 
promissory  notes  of  the  borrowers.  Now  a  loan  is 
really  an  exchange  of  money  for  a  promissory  note 
which  the  lender  —  in  this  case  the  bank  —  receives 
in  place  of  the  gold.  Let  us  suppose  that  so-called 
borrowers  actually  draw  out  S50,000  of  gold.  The 
bank  thereby  exchanges  money  for  promises,  and  its 
books  will  then  read :  — 


Assets 

Gold  reserve .     .     . 
Promissory  notes   . 


$50,000 
50,000 

$100,000 


Liabilities 

Due  depositor  A  .  , 
Due  depositor  B  .  , 
Due  other  depositors 


$  9,000 
11,000 
80,000 

$100,000 


It  will  be  noted  that  now  the  gold  in  the  bank  is 
only  $50,000,  while  the  total  deposits  are  still 
S100,000.  In  other  words,  the  depositors  now  have 
more  "'money  on  deposit"  than  the  bank  has  in  its 
vaults  !  But,  as  will  be  shown,  this  form  of  expression 
involves  a  popular  fallacy  in  the  word  ''money." 
Something  good  is  behind  each  loan,  but  not  necessarily 
money. 

Next,  suppose  that  the  borrowers  become,  in  a  sense, 
depositors  also,  by  redepositing  the  $50,000  of  cash 
which  they  borrowed,  in  return  for  the  right  to  draw  out 
the  same  sum  on  demand.     In  other  words,   suppose 


Sec.  1] 


DEPOSIT  CURRENCY 


37 


that  after  borrowing  $50,000  from  the  bank,  they  lend 
it  back  to  the  bank.  The  bank's  assets  will  thus  be 
enlarged  by  $50,000,  and  its  obligations  (or  credit 
extended)  will  be  equally  enlarged;  and  the  balance 
sheet  will  become :  — 


Assets 

Gold  reserve      .    . 
Promissory  notes    . 


iX 


Ct^ 


$100,000 
50,000 


$150,000 


Liabilities 

Due  depositor  A  .     . 
Due  depositor  B  .     . 
Due  old  depositors   . 
Due    new    depositors, 
i.e.  the  borrowers  . 


5  9,000 
11,000 
80,000 

50,000 
$150,000 


What  happened  in  this  case  was  the  following :  Gold 
was  borrowed  in  exchange  for  a  promissory  note  and 
then  handed  back  in  exchange  for  a  right  to  draw. 
Thus  the  gold  really  did  not  budge;  but  the  bank 
received  a  promissory  note  and  the  depositor  a  right  to 
draw.  Evidently,  therefore,  the  same  result  would  have 
followed  if  each  borrower  had  merely  handed  in  his  prom- 
issory note  and  received,  in  exchange,  a  right  to  draw. 
As  this  operation  most  frequently  puzzles  the  beginner 
in  the  study  of  banking,  we  repeat  the  tables  repre- 
senting the  conditions  before  and  after  these  ''loans," 
i.e.  these  exchanges  of  promissory  notes  for  present 
rights  to  draw.^ 

1  In  the  ultimate  analysis,  and  outside  of  its  function  of  insuring 
credit,  a  bank  is  really  an  intermediary  between  borrowers  and 
lenders.  It  is  by  virtue  of  bringing  borrowers  and  ultimate  lenders 
together  and  providing  the  former  with  a  supply  of  loans  which 
would  not  otherwise  exist,  that  a  bank  simultaneously  tends  to 
lower  the  rate  of  interest  and  increase  the  supply  of  credit  cur- 
rency. See  paper  by  Harry  G.  Brown,  in  the  Quarterly  Journal  of 
Economics,  August,  1910,  on  "Commercial  Banking  and  the  Rate  of 
Interest."  4  p  f*  I*  r* 


38  THE    PURCHASING   POWER   OF  MONEY     [Chap.  Ill 


Before  the  Loans 

Assets 

Liabilities 

Gold  reserve      .    . 

.    $100,000  1  Due  depositors     .     . 
After  the  Loans 

$100,000 

Gold  reserve .     .     . 
Promissory  notes    . 

.    $100,000 
50,000 

Due  depositors     .     . 

$150,000 

Clearly,  therefore,  the  intermediation  of  the  money  in 
this  case  is  a  needless  complication,  though  it  may  help 
to  a  theoretical  miderstanding  of  the  resultant  shifting 
of  rights  and  liabilities.  Thus  the  bank  may  receive 
deposits  of  gold  or  deposits  of  promises.  In  exchange 
for  the  promises  it  may  give,  or  lend,  either  a  right 
to  draw,  or  gold,  —  the  same  that  was  deposited  by 
another  customer.  Even  when  the  borrower  has 
only  a  promise,  by  fiction  he  is  still  held  to  have  de- 
posited money ;  and  like  the  original  cash  depositors,  he 
is  given  the  right  to  make  out  checks.  The  total  value 
of  rights  to  draw,  in  whichever  way  arising,  is  termed 
''deposits."  Banks  more  often  lend  rights  to  draw  (or 
deposit  rights)  than  actual  cash,  partly  because  of  the 
greater  convenience  to  borrowers,  and  partly  because 
the  banks  wish  to  keep  their  cash  reserves  large,  in  order 
to  meet  large  or  unexpected  demands.  It  is  true  that 
if  a  bank  loans  money,  part  of  the  money  so  loaned  will 
be  redeposited  by  the  persons  to  whom  the  borrowers 
pay  it  in*  the  course  of  business ;  but  it  will  not  neces- 
sarily be  redeposited  in  the  same  bank.  Hence  the 
average  banker  prefers  that  the  borrower  should  not 
withdraw  actual  cash. 

Besides  lending  deposit  rights,  banks  may  also  lend 
their  own  no^es,  called  ''bank  notes."  And  the 
principle  governing  bank  notes  is  the  same  as  the  prin- 


Sec.  1] 


DEPOSIT   CURRENCY 


39 


ciple  governing  deposit  rights.  The  holder  simply  gets 
a  pocketful  of  bank  notes  instead  of  a  bank  account. 
In  either  case  the  bank  must  be  always  ready  to  pay 
the  holder  —  to  ''redeem  its  notes"  —  as  well  as  pay 
its  depositors,  on  demand,  and  in  either  case  the  bank 
exchanges  a  promise  for  a  promise.  In  the  case  of  the 
note,  the  bank  has  exchanged  its  bank  note  for  a  cus- 
tomer's promissory  note.  The  bank  note  carries  no 
interest,  but  is  payable  on  demand.  The  customer's 
note  bears  interest,  but  is  payable  only  at  a  definite 
date. 

Assuming  that  the  bank  issues  $50,000  of  notes,  the 
balance  sheet  will  now  become  : —  .,   'L, 


Assets 

Gold  reserve .    .    .    .    $100,000 
Loans 100,000 


Liabilities 


$200,000 


Due  depositors     , 
Due  note  holders 


% 


$150,000 
50,000 

$200,000 


We  repeat  that  by  means  of  credit  the  deposits  (and 
notes)  of  a  bank  may  exceed  its  cash.  There  would 
be  nothing  mysterious  or  obscure  about  this  fact,  nor 
about  credit  in  general,  if  people  could  be  induced  not 
to  think  of  banking  operations  as  money  operations. 
To  so  represent  them  is  metaphorical  and  misleading. 
They  are  no  more  money  operations  than  they  are 
real  estate  transactions.  A  bank  depositor,  A,  has  not 
ordinarily  ''deposited  money";  and  whether  he  has 
or  not,  he  certainly  cannot  properly  say  that  he  "has 
money  in  the  bank."  What  he  does  have  is  the  bank's 
promise  to  pay  money  on  demand.  The  bank  owes  him 
money.  When  a  private  person  owes  money,  the 
creditor  never  thinks  of  saying  that  he  has  it  on  deposit 
in  the  debtor's  pocket. 


40  THE   PURCHASING    POWER   OF  MONEY    [Chap.  Ill 

§2 

It  cannot  be  too  strongly  emphasized  that,  in  any 
balance  sheet,  the  value  of  the  liabilities  rests  on  that 
of  the  assets.  The  deposits  of  a  bank  are  no  excep- 
tion. We  must  not  be  misled  by  the  fact  that  the 
cash  assets  may  be  less  than  the  deposits.  When 
the  uninitiated  first  learn  that  the  number  of  dol- 
lars which  note  holders  and  depositors  have  the  right 
to  draw  out  of  a  bank  exceeds  the  number  of  dollars 
in  the  bank,  they  are  apt  to  jump  to  the  conclusion 
that  there  is  nothing  behind  the  notes  or  deposit  liabil- 
ities. Yet  behind  all  these  obligations  there  is  always, 
in  the  case  of  a  solvent  bank,  full  value ;  if  not  actual 
dollars,  at  any  rate  dollars'  worth  of  property.  By  no 
jugglery  can  the  liabilities  exceed  the  assets  except  in 
insolvency,  and  even  in  that  case  only  nominally, 
for  the  true  value  of  the  liabiUties  (''bad  debts")  will 
only  equal  the  true  value  of  the  assets  behind  them. 

These  assets,  as  already  indicated,  are  largely  the 
notes  of  merchants,  although,  so  far  as  the  theory  of 
banking  is  concerned,  they  might  be  any  property 
whatever.  If  they  consisted  in  the  ownership  of  real 
estate  or  other  wealth  in  ''fee  simple,"  so  that  the 
tangible  wealth  which  property  always  represents 
were  clearly  evident,  all  mystery  would  disappear. 
But  the  effect  would  not  be  different.  Instead  of 
taking  grain,  machines,  or  steel  ingots  on  deposit,  in 
exchange  for  the  sums  lent,  banks  prefer  to  take  interest- 
bearing  notes  of  corporations  and  individuals  who  own, 
directly  or  indirectly,  grain,  machines,  and  steel  ingots  : 
and  by  the  banking  laws  the  banks  are  even  compelled 
to  take  the  notes  instead  of  the  ingots.  The  bank 
finds  itself  with  liabilities  which  exceed  its  cash  assets ; 


Sec.  2]  DEPOSIT  CURRENCY  41 

but  in  either  case  the  excess  of  habilities  is  balanced  by 
the  possession  of  other  assets  than  cash.  These  other 
assets  of  the  bank  are  usually  liabilities  of  business 
men.  These  liabilities  are  in  turn  supported  by  the 
assets  of  the  business  men.  If  we  continue  to  follow 
up  the  ultimate  basis  of  the  bank's  liabilities  we  shall 
find  it  in  the  visible  tangible  wealth  of  the  world. 

This  ultimate  basis  of  the  entire  credit  structure  is 
kept  out  of  sight,  but  the  basis  exists.  Indeed,  we  may 
say  that  banking,  in  a  sense,  causes  this  visible,  tangible 
wealth  to  circulate.  If  the  acres  of  a  landowner  or 
the  iron  stoves  of  a  stove  dealer  cannot  circulate  in  [y 
literally  the  same  way  that  gold  dollars  circulate,  yet 
the  landowner  or  stove  dealer  may  give  to  the  bank  a 
note  on  which  the  banker  may  base  bank  notes  or  de- 
posits ;  and  these  bank  notes  and  deposits  will  circulate 
like  gold  dollars.  Through  banking,  he  who  possesses 
wealth  difficult  to  exchange  can  create  a  circulating 
medium.  He  has  only  to  give  to  a  bank  his  note  —  for 
which,  of  course,  his  property  is  liable — get  in  return  the 
right  to  draw,  and  lo  !  his  comparatively  unexchange- 
able wealth  becomes  liquid  currency.  To  put  it  crudely, 
banking  is  a  device  for  coining  into  dollars  land,  stoves, 
and  other  wealth  not  otherwise  generally  exchangeable. 

It  is  interesting  to  observe  that  the  formation  of 
the  great  modern  ''trusts"  has  given  a  considerable 
impetus  to  deposit  currency ;  for  the  securities  of  large 
corporations  are  more  easily  used  as  ''collateral  se- 
curity" for  bank  loans  than  the  stocks  and  bonds  of 
small  corporations  or  than  partnership  rights. 

We  began  by  regarding  a  bank  as  substantially  a 
cooperative  enterprise,  run  for  the  convenience  and  at 
the  expense  of  its  depositors.  But,  as  soon  as  it  reaches 
the  point  of  lending  money  to  X,  Y ,  and  Z,  on  time, 


42  THE    PURCHASING   POWER   OF  MONEY    [Chap.  Ill 

while  itself  owing  money  on  demand,  it  assumes 
toward  X,  Y,  and  Z  and  its  cash  depositors  risks  which 
the  depositors  would  be  unwilling  to  assume.  To 
meet  this  situation,  the  responsibility  and  expense  of 
running  the  bank  are  taken  by  a  third  class  of  people  — 
stockholders  —  who  are  willing  to  assume  the  aug- 
mented risk  for  the  sake  of  the  chance  of  profit.  Stock- 
holders, in  order  to  guarantee  the  depositors  against  loss, 
put  in  some  cash  of  their  own.  Their  contract  is,  in 
effect,  to  make  good  any  loss  to  depositors.  Let  us  sup- 
pose that  the  stockholders  put  in  $50,000,  viz.  S40,000 
in  cash  and  $10,000  in  the  purchase  of  a  bank  building. 
The  accounts  now  stand  : — 

Assets  Liabilities 


Cash $140,000 

Loans 100,000 

Building 10,000 

$250,000 


Due  depositors  .  .  $150,000 
Due  note  holders  .  .  50,000 
Due  stockholders      .        50,000 


$250,000 


The  accounts  as  they  now  stand  include  the  chief  fea- 
tures of  an  ordinary  modern  bank,  —  a  so-called  "bank 
of  deposit,  issue,  and  discount." 


We  have  seen  that  the  assets  must  be  adequate  to  meet 
the  liabilities.  We  now  wish  to  point  out  that  the  form 
of  the  assets  must  be  such  as  will  insure  meeting  the  lia- 
bilities promptly.  Since  the  business  of  a  bank  is  to  fur- 
nish quickly  available  property  (cash  or  credit)  in  place 
of  the  "slower"  property  of  its  depositors,  it  fails  of  its 
purpose  when  it  is  caught  with  insufficient  cash.  Yet 
it  "makes money  "  partly  by  tying  up  its  quick  property, 
i.e.  lending  it  out  where  it  is  less  accessible.     Its  prob- 


Sec.  3]  DEPOSIT  CURRENCY  43 

lem  in  policy  is  to  tie  up  enough  to  increase  its  prop- 
erty, but  not  to  tie  up  so  much  as  to  get  tied  up  itself. 
So  far  as  anything  has  yet  been  said  to  the  contrary, 
a  bank  might  increase  indefinitely  its  loans  in  relation 
to  its  cash  or  in  relation  to  its  capital.  If  this  were 
so,    deposit    currency    could    be   indefinitely   inflated. 

There  are  limits,  however,  imposed  by  prudence  and 
sound  economic  policy,  on  both  these  processes.  In- 
solvency and  insufficiency  of  cash  must  both  be  avoided. 
Insolvency  is  that  condition  which  threatens  when  loans 
are  extended  with  insufficient  capital.  Insufficiency 
of  cash  is  that  condition  which  threatens  when  loans 
are  extended  unduly  relatively  to  cash.  Insolvency 
is  reached  when  assets  no  longer  cover  liabilities  (to 
others  than  stockholders),  so  that  the  bank  is  unable 
to  pay  its  debts.  Insufficienc}'^  of  cash  is  reached  when, 
although  the  bank's  total  assets  are  fully  equal  to  its 
liabilities,  the  actual  cash  on  hand  is  insufficient  to 
meet  the  needs  of  the  instant,  and  the  bank  is  unable 
to  pay  its  debts  on  demand. 

The  less  the  ratio  of  the  value  of  the  stockholders' 
interests  to  the  value  of  liabilities  to  others,  the  greater 
is  the  risk  of  insolvency;  the  risk  of  insufficiency  of 
cash  is  the  greater,  the  less  the  ratio  of  the  cash  to  the 
demand  liabilities.  In  other  words,  the  leading  safe- 
guard against  insolvency  lies  in  a  large  capital  and  sur- 
plus, but  the  leading  safeguard  against  insufficiency  of 
cash  lies  in  a  large  cash  reserve.  Insolvency  proper 
may  befall  any  business  enterprise ;  insufficiency  of 
cash  relates  especially  to  banks  in  their  function  of 
redeeming  notes  and  deposits. 

Let  us  illustrate  insufficiency  of  cash.  In  our  bank's 
accounts  as  we  left  them,  there  was  a  reserve  of  $140,000 
of  cash,  and  $200,000  of  demand  liabilities  (deposits 


44  THE    PURCHASING   POWER   OF   MONEY     [Chap.  Ill 

and  notes).  The  managers  of  the  bank  may  think 
this  reserve  of  $140,000  unnecessarily  large  or  the  loans 
unnecessarily  small.  They  may  then  extend  their  loans 
(extended  to  customers  in  the  form  of  cash,  notes  or 
deposit  accounts)  until  the  cash  reserve  is  reduced, 
say  to  $40,000,  and  the  liabihties  due  depositors  and  note 
holders  increased  to  $300,000.  If,  under  these  cir- 
cumstances, some  depositor  or  note  holder  demands 
$50,000  cash,  immediate  payment  will  be  impossible. 
It  is  true  that  the  assets  still  equal  the  liabilities.  There 
is  full  value  behind  the  $50,000  demanded ;  but  the 
understanding  was  that  depositors  and  note  holders 
should  be  paid  in  money  and  on  demand.  Were  this 
not  a  stipulation  of  the  deposit  contract,  the  bank 
might  pay  the  claims  thus  made  upon  it  by  transfer- 
ring to  its  creditors  the  promissory  notes  due  it  from 
its  debtors  ;  or  it  might  ask  the  customers  to  wait  until 
it  could  turn  these  securities  into  cash.f. 

Since  a  bank  cannot  follow  either  of  these  plans,  it 
tries,  where  insufficiency  of  cash  impends,  to  forestall  this 
condition  by  "calling  in"  some  of  its  loans,  or  if  none 
can  be  called  in,  by  selling  some  of  its  securities  or  other 
property  for  cash.  But  it  happens  unfortunately  that 
there  is  a  limit  to  the  amount  of  cash  which  a  bank 
can  suddenly  realize.  No  bank  could  escape  failure  if 
a  large  percentage  of  its  note  holders  and  depositors 
should  simultaneously  demand  cash  payment.-  The 
paradox  of  a  panic  is  well  expressed  by  the  case  of 
the  man  who  inquired  of  his  bank  whether  it  had  cash 
available  for  paying  the  amount  of  his  deposit,  saying, 
"If  you  can  pay  me,  I  don't  want  it ;  but  if  you  can't, 

^  See  Irving  Fisher,  The  Nature  of  Capital  and' Income,  Chapter  V. 
2Cf.  Ricardo,   Works,  2d  ed.,  London  (Murray),   1852,  p.  217 
{Principles  of  Political  Economy  and  Taxation,  Chapter  XXVII). 


Sec.  3]  DEPOSIT  CURRENCY  45 

I  do."  Such  was  the  situation  in  1907  in  Wall  Street. 
All  the  depositors  at  one  time  wanted  to  be  sure  their 
money ' '  was  there. ' '    Yet  it  never  is  there  all  at  one  time. 

Since,  then,  insufficiency  of  cash  is  so  troublesome 
a  condition,  —  so  difficult  to  escape  when  it  has  arrived, 
and  so  difficult  to  forestall  when  it  begins  to  ap- 
proach, —  a  bank  must  so  regulate  its  loans  and  note 
issues  as  to  keep  on  hand  a  sufficient  cash  reserve,  and 
thus  prevent  insufficiency  of  cash  from  even  threaten- 
ing. It  can  regulate  the  reserve  by  alternately  selling 
securities  for  cash  and  loaning  cash  on  securities.  The 
more  the  loans  in  proportion  to  the  cash  on  hand, 
the  greater  the  profits,  but  the  greater  the  danger  also. 
In  the  long  run  a  bank  maintains  its  necessary  reserve 
by  means  of  adjusting  the  interest  rate  charged  for 
loans.  If  it  has  few  loans  and  a  reserve  large  enough  to 
support  loans  of  much  greater  volume,  it  will  endeavor 
to  extend  its  loans  by  lowering  the  rate  of  interest. 
If  its  loans  are  large  and  it  fears  too  great  demands 
on  the  reserve,  it  will  restrict  the  loans  by  a  high  interest 
charge.  Thus,  by  alternately  raising  and  lowering  in- 
terest, a  bank  keeps  its  loans  within  the  sum  which  the 
reserve  can  support,  but  endeavors  to  keep  them  (for 
the  sake  of  profit)  as  high  as  the  reserve  will  support. 

If  the  sums  owed  to  individual  depositors  are  large, 
relatively  to  the  total  liabilities,  the  reserve  should  be 
proportionately  large,  since  the  action  of  a  small  num- 
ber of  depositors  can  deplete  it  rapidly.^  Similarly,  the 
reserves  should  be  larger  against  fluctuating  deposits 
(as  of  stock  brokers)  or  those  known  to  be  temporary.^ 

'  Victor  Morawetz,  The  Banking  and  Currency  Problem  in  the 
United  States,  New  York  (The  North  American  Review  Publish- 
ing Co.),  1909,  pp.  36  and  37.  Also  Kem merer,  Money  and  Prices, 
1909,  p.  80.  2  Ibid. 


46  THE    PURCHASING   POWER   OF  MONEY     [Chap.  Ill 

The  reserve  in  a  large  city  of  great  bank  activity  needs 
to  be  greater  in  proportion  to  its  demand  liabilities  than 
in  a  small  town  with  infrequent  banking  transactions. 

Experience  dictates  differently  the  average  size  of 
deposit  accounts  for  different  banks  according  to  the 
general  character  and  amount  of  their  business.  For 
every  bank  there  is  a  normal  ratio,  and  hence  for  a 
whole  community  there  is  also  a  normal  ratio  —  an 
average  of  the  ratios  for  the  different  banks.  No 
absolute  numerical  rule  can  be  given.  Arbitrary  rules 
are  often  imposed  by  law.  National  banks  in  the 
United  States,  for  instance,  are  required  to  keep  a  re- 
serve for  their  deposits,  varying  according  as  they  are 
or  are  not  situated  in  certain  cities  designated  by  law 
as  ''reserve"  cities,  i.e.  cities  where  national  banks 
hold  deposits  of  banks  elsewhere.  These  reserves  are 
all  in  defense  of  deposits.  In  defense  of  notes,  on 
the  other  hand,  no  cash  reserve  is  required,  —  that  is, 
of  national  banks.  True,  the  same  economic  princi- 
ples apply  to  both  bank  notes  and  deposits,  but  the  law 
treats  them  differently.  The  government  itself  chooses 
to  undertake  to  redeem  the  national  bank  notes  on 
demand. 

The  state  banks  are  subject  to  varying  restrictions.^ 
Thus  the  requirement  as  to  the  ratio  of  reserve  to  de- 
posits varies  from  12|  per  cent  to  22^  per  cent,  being 
usually  between  15  per  cent  and  20  per  cent.  Of  the 
reserve,  the  part  which  must  be  cash  varies  from  10  per 
cent  (of  the  reserve)  to  50  per  cent,  being  usually  40 
per  cent. 

Such  legal  regulation  of  banking  reserves,  however, 

*  "Digest  of  State  Banking  Statutes,"  in  Reports  of  the  National 
Monetary  Commission,  61st  Congress,  2d  Session  Senate  Document, 
No.  353. 


Sec.  4]  DEPOSIT  CURRENCY  47 

is  not  a  necessary  development  of  banking.  In  Can- 
ada, the  law  makes  the  notes  practically  coordinate 
with  the  deposits.  Indeed,  banking  may  exist  with- 
out government  regulations  at  all.  ''George  Smith's 
money  "  furnishes  an  illustration.  George  Smith,  Alex- 
ander Mitchell  and  others  established  in  1839  an 
Insurance  Company  which,  though  forbidden  to  exer- 
cise "banking  privileges,"  issued  certificates  of  deposit 
payable  to  bearer,  and  these  certificates  were  actually 
circulated  like  bank  notes. ^ 

§4 

The  study  of  banking  operations,  then,  discloses  two 
species  of  currency :  one,  bank  notes,  belonging  to 
the  category  of  money;  and  the  other,  deposits,  be- 
longing outside  of  that  category,  but  constituting  an 
excellent  substitute.  Referring  these  to  the  larger 
category  of  goods,  we  have  a  threefold  classification 
of  goods :  first,  money ;  second,  deposit  currency,  or 
simply  deposits  ;  and  third,  all  other  goods.  And  by 
the  use  of  these,  there  are  six  possible  types  of  ex- 
change :  — 

(1)  Money  against  money, 

(2)  Deposits  against  deposits, 

(3)  Goods  against  goods, 

(4)  Money  against  deposits, 

(5)  Money  against  goods, 

(6)  Deposits  against  goods. 

For  our  purpose,  only  the  last  two  types  of  exchange 
are  important,  for  these  constitute  the  circulation  of 
currency.  As  regards  the  other  four,  the  first  and  third 
have  been  previously  explained  as  "money  changing" 
and   "barter"   respectively.     The   second   and   fourth 

*  See  Horace  White,  Money  and  Banking 


48  THE    PURCHASING   POWER   OF  MONEY     [Chap.  Ill 

are  banking  transactions :  the  second  being  such  as 
the  selling  of  drafts  for  checks,  or  the  mutual  cancel- 
lation of  bank  clearings;  and  the  fourth  being  such 
operations  as  the  depositing  or  the  withdrawing  of 
money,  by  depositing  cash  or  cashing  checks. 

The  analysis  of  the  balance  sheets  of  banks  has  pre- 
pared us  for  the  inclusion  of  bank  deposits  or  circulating 
credit  in  the  equation  of  exchange.  We  shall  still  use 
M  to  express  the  quantity  of  actual  money,  and  V  to 
express  the  velocity  of  its  circulation.  Similarly,  we 
shall  now  use  M'  to  express  the  total  deposits  subject 
to  transfer  by  check ;  and  7'  to  express  the  average 
velocity  of  circulation.  The  total  value  of  purchases 
in  a  year  is  therefore  no  longer  to  be  measured  by  MV, 
but  by  MV  +  M'V.  The  equation  of  exchange,  there- 
fore, becomes :  — 

MV  +  M'V  =  2pQ  =  PT} 

Let  us  again  represent  the  equation  of  exchange  by 
means  of  a  mechanical  picture.     In  Figure  4,  trade, 


^Tr^H.M.^„.,|,„,j,.,n_„in,..,j_.„,|,„,||i,.jiii,jii,ij.|.,j,M,j^ 


Fig.  4. 

as  before,  is  represented  on  the  right  by  the  weight  of 
a  miscellaneous  assortment  of  goods ;  and  their  average 
price  by  the  distance  to  the  right  from  the  fulcrum,  or 

1  The  equation  of  exchange  is  also  stated  by  Kemmerer,  Money 
and  Credit  Instruments  in  their  Relation  to  General  Prices,  so  as  to 
inelude  bank  credit,  although  in  a  somewhat  different  way.  That 
credit  acts  on  prices  in  the  same  manner  as  money  is  by  no  means 
a  newly  established  principle.  See,  for  example,  MiU,  Principles  oj 
Political  Economy,  Book  III,  Chapter  XII,  §§  1,  2. 


Sec.  5]  DEPOSIT   CURRENCY  49 

the  length  of  the  arm  on  which  this  weight  hangs. 
Again  at  the  left,  money  (ikf )  is  represented  by  a  weight 
in  the  form  of  a  purse,  and  its  velocity  of  circulation  ( V) 
by  its  arm ;  but  now  we  have  a  new  weight  at  the  left, 
in  the  form  of  a  bank  book,  to  represent  the  bank  de- 
posits {M').  The  velocity  of  circulation  (V)  of  these 
bank  deposits  is  represented  by  its  distance  from  the 
fulcrum  or  the  arm  at  which  the  book  hangs. 

This  mechanism  makes  clear  the  fact  that  the  average 
price  (right  arm)  increases  with  the  increase  of  money  or 
bank  deposits  and  with  the  velocities  of  their  circulation, 
and  decreases  with  the  increase  in  the  volume  of  trade. 

Recurring  to  the  left  side  of  the  equation  of  exchange, 
OT  MV  +  M'V,  we  see  that  in  a  community  without 
bank  deposits  the  left  side  of  the  equation  reduces 
simply  to  MV,  the  formula  used  in  Chapter  II ;  for 
in  such  a  community  the  term  "  M'V  "  vanishes.  The 
introduction  of  M'  tends  to  raise  prices.  That  is,  the 
hanging  of  the  bank  book  on  the  left  requires  a  lengthen- 
ing of  the  arm  at  the  right. 

Just  as  E  was  used  to  denote  the  total  circulation 
of  money,  MV,  so  we  may  now  use  E'  to  denote  the 
total  circulation  of  deposits,  M'V. 

Like  E,  M,  and  V,  so  also  E',  M',  and  V  are  sums 
and  averages  of  corresponding  magnitudes  pertaining 
to  different  parts  of  the  year,  or  different  persons.^ 

§5 

With  the  extension  of  the  equation  of  monetary 
circulation  to  include  deposit  cii'culation,  the  influence 

1  The  mathematical  analysis  of  E',  M',  and  V  in  terms  of 
"arrays"  of  e"s,  m"s,  and  t;"s,  etc.,  is  precisely  parallel  to  that  of 
E,  M,  and  V,  given  in  the  Appendix  to  Chapter  II.  See  also  §§1 
and  2  of  Appendix  to  (this)  Chapter  III. 


50  THE    PURCHASING   POWER   OF   MONEY     [Chap.  IH 

exerted  by  the  quantity  of  money  on  general  prices 
becomes  less  direct ;  and  the  process  of  tracing  this 
influence  becomes  more  difficult  and  complicated.  It 
has  even  been  argued  that  this  interposition  of  circulating 
credit  breaks  whatever  connection  there  may  be  be- 
tween prices  and  the  quantity  of  money.  ^  This  would 
be  true  if  circulating  credit  were  independent  of  money. 
But  the  fact  is  that  the  quantity  of  circulating  credit,  M' , 
tends  to  hold  a  definite  relation  to  M,  the  quantity  of 
money  in  circulation;  that  is,  deposits  are  normally 
a  more  or  less  definite  multiple  of  money. 

Two  facts  normally  give  deposits  a  more  or  less 
definite  ratio  to  money.  The  first  has  been  already 
explained,  viz.  that  bank  reserves  are  kept  in  a  more 
or  less  definite  ratio  to  bank  deposits.  The  second 
is  that  individuals,  firms,  and  corporations  preserve 
more  or  less  definite  ratios  between  their  cash  trans- 
actions and  their  check  transactions,  and  also  between 
their  money  and  deposit  balances.^  These  ratios  are 
determined  by  motives  of  individual  convenience  and 
habit.  In  general,  business  firms  use  money  for  wage 
payments,  and  for  small  miscellaneous  transactions 
included  under  the  term  ''petty  cash";  while  for 
settlements  with  each  other  they  usually  prefer 
checks.  These  preferences  are  so  strong  that  we 
could   not  imagine   them  overridden  except  tempora- 

1  An  almost  opposite  view  is  that  of  Laughlin  that  normal  credit 
cannot  affect  prices  because  it  is  not  an  offer  of  standard  money  and 
cannot  affect  the  value  of  the  standard  which  alone  determines  general 
prices.  See  the  Principles  of  Money,  New  York  (Seribner),  1903,  p.  97. 
Both  views  are  inconsistent  with  that  upheld  in  this  book. 

2  This  fact  is  apparently  overlooked  by  Laughlin  when  he  argues 
that  there  is  not  "any  reason  for  limiting  the  amount  of  the  deposit 
currency,  or  the  assumption  of  an  absolute  scarcity  of  specie  re- 
serves."     See  Principles  of  Money,  p.  127. 


Sec.  5]  DEPOSIT  CURRENCY  51 

rily  and  to  a  small  degree.  A  business  firm  would 
hardly  pay  car  fares  with  checks  and  liquidate  its 
large  liabilities  with  cash.  Each  person  strikes  an 
equilibrium  between  his  use  of  the  two  methods  of 
payment,  and  does  not  greatly  disturb  it  except  for 
short  periods  of  time.  He  keeps  his  stock  of  money 
or  his  bank  balance  in  constant  adjustment  to  the 
payments  he  makes  in  money  or  by  check.  Whenever 
his  stock  of  money  becomes  relatively  small  and  his 
bank  balance  relatively  large,  he  cashes  a  check.  In 
the  opposite  event,  he  deposits  cash.  In  this  way 
he  is  constantly  converting  one  of  the  two  media  of 
exchange  into  the  other.  A  private  individual  usually 
feeds  his  purse  from  his  bank  account ;  a  retail  com- 
mercial firm  usually  feeds  its  bank  account  from  its 
till.     The  bank  acts  as  intermediary  for  both. 

In  a  given  community  the  quantitative  relation  of 
deposit  currency^  to  money  is  determined  by  several 
considerations  of  convenience.  In  the  first  place,  the 
more  highly  developed  the  business  of  a  community, 
the  more  prevalent  the  use  of  checks.  Where  business 
is  conducted  on  a  large  scale,  merchants  habitually 
transact  their  larger  operations  with  each  other  by 
means  of  checks,  and  their  smaller  ones  by  means  of 
cash.  Again,  the  more  concentrated  the  population, 
the  more  prevalent  the  use  of  checks.  In  cities  it  is 
more  convenient  both  for  the  payer  and  the  payee  to 
make  large  payments  by  check ;  whereas,  in  the  coun- 
try, trips  to  a  bank  are  too  expensive  in  time  and  effort 
to  be  convenient,  and  therefore  more  money  is  used 
in  proportion  to  the  amount  of  business  done.^     Again, 

1  The  convenient  expression  "deposit  currency"  is  used  by 
Laughlin,  The  Principles  of  Money,  p.  118. 

*  See   Kinley's    "Credit   Instruments,"    Report   of  the   National 


52  THE    PURCHASING   POWER   OF  MONEY    [Chap.  Ill 

the  wealthier  the  members  of  the  community,  the  more 
largely  will  they  use  checks.  Laborers  seldom  use 
them;  but  capitalists,  professional  and  salaried  men 
use  them  habitually,  for  personal  as  well  as  business 
transactions. 

There  is,  then,  a  relation  of  convenience  and  custom 
between  check  and  cash  circulation,  and  a  more  or  less 
stable  ratio  between  the  deposit  balance  of  the  average 
man  or  corporation  and  the  stock  of  money  kept  in 
pocket  or  till.  This  fact,  as  applied  to  the  country 
as  a  whole,  means  that  by  convenience  a  rough  ratio 
is  fixed  between  M  and  M'.  If  that  ratio  is  disturbed 
temporarily,  there  will  come  into  play  a  tendency  to 
restore  it.  Individuals  will  deposit  surplus  cash,  or 
they  will  cash  surplus  deposits. 

Hence,  both  money  in  circulation  (as  shown 
above)  and  money  in  reserve  (as  shown  previously) 
tend  to  keep  in  a  fixed  ratio  to  deposits.  It  follows 
that  the  two  must  be  in  a  fixed  ratio  to  each 
other. 

It  further  follows  that  any  change  in  M,  the  quantity 
of  money  in  circulation,  requiring  as  it  normally  does 
a  proportional  change  in  M',  the  volume  of  bank  de- 
posits subject  to  check,  will  result  in  an  exactly  pro- 
portional change  in  the  general  level  of  prices  except, 
of  course,  so  far  as  this  effect  be  interfered  with  by 
concomitant  changes  in  the  F's  or  the  Q's.  The 
truth  of  this  proposition  is  evident  from  the  equation 
MV  +  M'V  =^pQ;  for  if,  say,  M  and  M'  are 
doubled,  while  V  and  F'  remain  the  same,  the  left 
side  of  the  equation  is  doubled  and  therefore  the  right 
side  must  be  doubled   also.     But  if  the  Q's   remain 

Monetary  Commission,  Senate  Document,  399,  61st  Congress,  2d 
Session,  1910,  p.  188. 


Sec.  6]  DEPOSIT  CURRENCY  53 

unchanged,  then  evidently  all  the  p's  must  be  doubled, 
or  else  if  some  are  less  than  doubled,  others  must  be 
enough  more  than  doubled  to  compensate. 

§6 

The  contents  of  this  chapter  may  be  formulated  in 
a  few  simple  propositions  :  — 

(1)  Banks  supply  two  kinds  of  currency,  viz.  bank 
notes  —  which  are  money ;  and  bank  deposits  (or 
rights  to  draw)  —  which  are  not  money. 

(2)  A  bank  check  is  merely  a  certificate  of  a  right 
to  draw. 

(3)  Behind  the  claims  of  depositors  and  note  holders 
stand,  not  simply  the  cash  reserve,  but  all  the  assets  of 
the  bank. 

(4)  Deposit  banking  is  a  device  by  which  wealth, 
incapable  of  direct  circulation,  may  be  made  the  basis 
of  the  circulation  of  rights  to  draw. 

(5)  The  basis  of  such  circulating  rights  to  draw  or 
deposits  must  consist  in  part  of  actual  money,  and  it 
should  consist  in  part  also  of  quick  assets  readily  ex- 
changeable for  money. 

(6)  Six  sorts  of  exchange  exist  among  the  three  classes 
of  goods,  money,  deposits,  and  other  goods.  Of  these 
six  sorts  of  exchange,  the  most  important  for  our  pres- 
ent purposes  are  the  exchanges  of  money  and  deposits 
against  goods. 

(7)  The  equation  of  money  circulation  extended  so 
as  to  include  bank  deposits  reads  thus :  — 

MV  +  M'V  =  ^pQ  or  PT. 

(8)  There  tends  to  be  a  normal  ratio  of  bank  deposits 
(ilf' )  to  the  quantity  of  money  {M) ;  because  business 


C^ 


54  THE   PURCHASING    POWER   OF  MONEY    [Chap.  Ill 

convenience  dictates  that  the  available  currency  shall 
be  apportioned  between  deposits  and  money  in  a  cer- 
tain more  or  less  definite,  even  though  elastic,  ratio. 

(9)  The  inclusion  of  deposit  currency  does  not  nor- 
mally disturb  the  quantitative  relation  between  money 
and  prices. 


CHAPTER  IV 

DISTURBANCE  OF  EQUATION  AND  OF  PURCHASING   POWER 
DURING   TRANSITION   PERIODS 


In  the  last  chapter  it  was  shown  that  the  quantity 
of  bank  deposits  normally  maintains  a  definite  ratio 
to  the  quantity  of  money  in  circulation  and  to  the 
amount  of  bank  reserves.  As  long  as  this  normal 
relation  holds,  the  existence  of  bank  deposits  merely 
magnifies  the  effect  on  the  level  of  prices  produced  by 
the  quantity  of  money  in  circulation  and  does  not  in 
the  least  distort  that  effect.  Moreover,  changes  in 
velocity  or  trade  will  have  the  same  effect  on  prices, 
whether  bank  deposits  are  included  or  not. 

But  during  periods  of  transition  this  relation  between 
money  (M)  and  deposits  (M')  is  by  no  means  rigid. 

We  are  now  ready  to  study  these  periods  of  transition. 
The  change  which  constitutes  a  transition  may  be 
a  change  in  the  quantity  of  money,  or  in  any  other  factor 
of  the  equation  of  exchange,  or  in  all.  Usually  all  are 
involved,  but  the  chief  factor  which  we  shall  select  for 
study  (together  with  its  effect  on  the  other  factors) 
is  quantity  of  money.  If  the  quantity  of  money 
were  suddenly  doubled,  the  effect  of  the  change  would 
not  be  the  same  at  first  as  later.  The  ultimate  effect 
is,  as  we  have  seen,  to  double  prices ;  but  before  this 
happens,  the  prices  oscillate  up  and  down.  In  this 
chapter  we  shall  consider  the  temporary  effects  during 

55 


56  THE    PURCHASING   POWER   OF   MONEY     [Chap.  IV 

the  period  of  transition  separately  from  the  permanent 
or  ultimate  effects  which  were  considered  in  the  last 
chapter.  These  permanent  or  ultimate  effects  follow 
after  a  new  equilibrium  is  established,  —  if,  indeed, 
such  a  condition  as  equilibrium  may  be  said  ever  to 
be  established.  What  we  are  concerned  with  in  this 
chapter  is  the  temporary  effects,  i.e.  those  in  the  tran- 
sition period. 

The  transition  periods  may  be  characterized  either  by 
rising  prices  or  by  falling  prices.  Rising  prices  must 
be  clearly  distinguished  from  high  prices,  Suiid  falling  from 
low.  With  stationary  levels,  high  or  low,  we  have  in 
this  chapter  nothing  to  do.  Our  concern  is  with  ris- 
ing or  falling  prices.  Rising  prices  mark  the  transition 
between  a  low  and  a  high  level  of  prices,  just  as  a  hill 
marks  the  transition  between  flat  lowlands  and  flat 
highlands. 

Since  the  study  of  these  acclivities  and  declivities 
is  bound  up  with  that  of  the  adjustment  of  interest 
rates,  our  first  task  is  to  present  a  brief  statement 
regarding  the  effects  of  rising  and  falling  prices^  on 
the  rate  of  interest.  Indeed,  the  chief  object  of  this 
chapter  is  to  show  that  the  peculiar  behavior  of  the 
rate  of  interest  during  transition  periods  is  largely 
responsible  for  the  crises  and  depressions  in  which  price 
movements  end. 

It  must  be  borne  in  mind  that  although  business  loans 
are  made  in  the  form  of  money,  yet  whenever  a  man 
borrows  money,  he  does  not  do  this  in  order  to  hoard 
the  money,  but  to  purchase  goods  with  it.  To  all 
intents  and  purposes,  therefore,  when  A  borrows  one 
hundred  dollars  from  B  in  order  to  purchase,  say,  one 

'  For  a  fuller  statement,  see  Irving  Fisher,  The  Rate  of  Interest, 
New  York  (Macmillan),  1907,  Chapters  V,  XIV. 


Sec.  1]  TRANSITION   PERIODS  57 

hundred  units  of  a  given  commodity  at  one  dollar  per 
unit,  it  may  be  said  that  B  is  virtually  lending  A  one 
hundred  units  of  that  commodity.  And  if  at  the  end 
of  a  year  A  returns  one  hundred  dollars  to  B,  but  the 
price  of  the  commodity  has  meanwhile  advanced,  then  B 
has  lost  a  fraction  of  the  purchasing  power  originally 
loaned  to  A.  For  even  though  A  should  happen  to 
return  to  B  the  identical  coins  in  which  the  loan  was 
made,  these  coins  represent  somewhat  less  than  the 
original  quantity  of  purchasable  commodities.  Bear- 
ing this  in  mind  in  our  investigation  of  interest  rates, 
let  us  suppose  that  prices  are  rising  at  the  rate  of  3  per 
cent  each  year.  It  is  plain  that  the  man  who  lends  $100 
at  the  beginning  of  the  year  must,  in  order  to  get  5  per 
cent  interest  in  purchasing  power,  receive  back  both 
$103  (then  the  equivalent  of  the  $100  lent)  plus  5  per 
cent  of  this,  or  a  total  of  $108.15.  That  is,  in  order  to 
get  5  per  cent  interest  in  actual  purchasing  power,  he 
must  receive  a  little  more  than  8  per  cent  interest  in 
money.  The  3  per  cent  rise  of  prices  thus  ought  to  add 
approximately  3  per  cent  to  the  rate  of  interest.  Rising 
prices,  therefore,  in  order  that  the  relations  between 
creditor  and  debtor  shall  be  the  same  during  the  rise 
as  before  and  after,  require  higher  money  interest  than 
stationary  prices  require. 

Not  only  will  lenders  require,  but  borrowers  can  afford 
to  pay  higher  interest  in  terms  of  money ;  and  to  some 
extent  competition  will  gradually  force  them  to  do  so.' 
Yet  we  are  so  accustomed  in  our  business  dealings  to 
consider  money  as  the  one  thing  stable,  —  to  think  of 
a  "dollar  as  a  dollar"  regardless  of  the  passage  of  time, 
that  we  reluctantly  yield  to  this  process  of  readjustment, 
thus  rendering  it  very  slow  and  imperfect.     When  prices 

^  Rate  o/  Interest,  Chapter  XIV. 


58  THE    PURCHASING   POWER  OF  MONEY     [Chap.  IV 

are  rising  at  the  rate  of  3  per  cent  a  year,  and  the  nor- 
mal rate  of  interest  —  i.e.  the  rate  which  would  exist  were 
prices  stationary  —  is  5  per  cent,  the  actual  rate,  though 
it  ought  (in  order  to  make  up  for  the  rising  prices)  to 
be  8.15  per  cent,  will  not  ordinarily  reach  that  figure; 
but  it  may  reach,  say,  6  per  cent,  and  later,  7  per  cent. 
This  inadequacy  and  tardiness  of  adjustment  are  fostered, 
moreover,  by  law  and  custom,  which  arbitrarily  tend  to 
keep  down  the  rate  of  interest. 

A  similar  inadequacy  of  adjustment  is  observed  when 
prices  are  falling.  Suppose  that,  by  the  end  of  a  year, 
$97  will  buy  as  much  as  $100  at  the  beginning.  In  that 
case  the  lender,  in  order  to  get  back  a  purchasing  power 
equivalent  to  his  principal  and  5  per  cent  interest, 
should  get,  not  $105,  but  only  $97  +  5  per  cent  of  $97 
or  $101.85.  Thus  the  rate  of  interest  in  money  should 
in  this  case  be  1.85  per  cent,  or  less  than  2  per  cent, 
instead  of  the  original  5  per  cent.  In  other  words,  the 
3  per  cent  fall  of  prices  should  reduce  the  rate  of  interest 
by  approximately  3  per  cent.  But  as  a  matter  of  fact, 
such  a  perfect  adjustment  is  seldom  reached,  and  money 
interest  keeps  far  above  2  per  cent  for  a  considerable 
time.^ 

§2 

We  are  now  ready  to  study  temporary  or  transitional 
changes  in  the  factors  of  our  equation  of  exchange.  Let 
us  begin  by  assuming  a  slight  initial  disturbance,  such 
as  would  be  produced,  for  instance,  by  an  increase  in  the 
quantity  of  gold.  This,  through  the  equation  of  ex- 
change, will  cause  a  rise  in  prices.  As  prices  rise, 
profits  of  business  men,  measured  in  money,  will  rise 
also,  even  if  the  costs  of  business  were  to  rise  in  the  same 

*  Rate  of  Interest,  loc.  cit. 


Sec.  2]  TRANSITION    PERIODS  59 

proportion.  Thus,  if  a  man  who  sold  $10,000  of  goods 
at  a  cost  of  $6000,  thus  clearing  $4000,  could  get  double 
prices  at  double  cost,  his  profit  would  be  double  also, 
being  $20,000  -  $12,000,  which  is  $8000.  Of  course 
such  a  rise  of  prices  would  be  purely  nominal,  as  it 
would  merely  keep  pace  with  the  rise  in  price  level. 
The  business  man  would  gain  no  advantage,  for  his 
larger  money  profits  would  buy  no  more  than  his  former 
smaller  money  profits  bought  before.  But,  as  a  matter 
of  fact,  the  business  man's  profits  will  rise  more  than  this 
because  the  rate  of  interest  he  has  to  pay  will  not  ad- 
just itself  immediately.  Among  his  costs  is  interest, 
and  this  cost  will  not,  at  first,  rise.  Thus  the  profits  will 
rise  faster  than  prices.  Consequently,  he  will  find  him- 
self making  greater  profits  than  usual,  and  be  en- 
couraged to  expand  his  business  by  increasing  his  bor- 
rowings. These  borrowings  are  mostly  in  the  form  of 
short-time  loans  from  banks;  and,  as  we  have  seen, 
short-time  loans  engender  deposits.  As  is  well  known, 
the  correspondence  between  loans  and  deposits  is  re- 
markably exact. ^  Therefore,  deposit  currency  (M')  will 
increase,  but  this  extension  of  deposit  currency  tends 
further  to  raise  the  general  level  of  prices,  just  as  the  in- 
crease of  gold  raised  it  in  the  first  place.^  Hence  prices, 
which  were  already  outstripping  the  rate  of  interest, 
tend  to    outstrip  it    still  further,  enabling  borrowers, 

^  See  J.  Pease  Norton,  Statistical  Studies  in  the  New  York  Money 
Market  (Macmillan),  1902,  chart  at  end. 

*  See  article  by  Knut  Wicksell  in  the  Jahrbucher  fur  National- 
ohoiomie,  1897  (Band  68),  pp.  228-243,  entitled  "Der  Bankzins  als 
Rej^ulator  der  Warenpreise."  This  article,  while  not  dealing  di- 
rectly with  credit  cycles  as  related  to  panics,  points  out  the  con- 
nection between  the  rate  of  interest  on  bank  loans  and  changes 
ii  Ithe  level  of  prices  due  to  the  resulting  expansion  and  contraction 
of^uch  loans. 


60  THE   PURCHASING    POWER   OF  MONEY     [Chap.  IV 

who  were  already  increasing  their  profits,  to  increase 
them  still  further.  More  loans  are  demanded,  and 
although  nominal  interest  may  be  forced  up  some- 
what, still  it  keeps  lagging  below  the  normal  level. 
Yet  nominally  the  rate  of  interest  has  increased; 
and  hence  the  lenders,  too,  including  banks,  are  led  to 
become  more  enterprising.  Beguiled  by  the  higher 
nominal  rates  into  the  belief  that  fairly  high  interest 
is  being  realized,  they  extend  their  loans,  and  with  the 
resulting  expansion  of  bank  loans,  deposit  currency 
(M'),  already  expanded,  expands  still  more.  Also,  if 
prices  are  rising,  the  money  value  of  collateral  may  be 
greater,  making  it  easier  for  borrowers  to  get  large 
credit.^  Hence  prices  rise  still  further.^  This  sequence 
of  events  may  be  briefly  stated  as  follows  :  — 

1.  Prices  rise  (whatever  the  first  cause  may  be;  but 
we  have  chosen  for  illustration  an  increase  in  the  amount 
of  gold). 

2.  The  rate  of  interest  rises,  but  not  sufficiently. 

3.  Enterprisers  (to  use  Professor  Fetter's  term),  en- 
couraged by  large  profits,  expand  their  loans. 

4.  Deposit  currency  (M')  expands  relatively  to 
money  (M). 

5.  Prices  continue  to  rise,  that  is,  phenomenoin  No.  1 
is  repeated.     Then  No.  2  is  repeated,  and  so  on. 

In  other  words,  a  slight  initial  rise  of  prices  sets  in 
motion  a  train  of  events  which  tends  to  repeat  itself. 
Rise  of  prices  generates  rise  of  prices,  and  continues 
to  do  so  as  long  as  the  interest  rate  lags  behind  its  normal 
figure. 

1  See  Kinley,  Money,  New  York  (Maomillan),  1904,  p.  223. 
*  See  Wicksell,  op.  cit. 

I 
'i 


Sec.  3J  TRANSITION   PERIODS  61 

§3 

The  expansion  of  deposit  currency  indicated  in  this 
cumulative  movement  abnormally  increases  the  ratio  of 
M'  to  M.  This  is  evident  if  the  rise  of  prices  begins  in 
a  change  in  some  element  or  elements  in  the  equation 
other  than  the  quantity  of  money ;  for  if  M  remains 
constant  and  M'  increases,  the  ratio  M'  to  M  must  in- 
crease also.  If  M  increases  in  any  ratio,  M'  will  increase 
in  a  greater  ratio.  If  it  increased  only  in  the  same  ratio, 
prices  would  increase  in  that  ratio  (assuming  velocities 
and  quantities  unchanged);  and  if  prices  increased  in 
that  ratio,  loans  (which  being  made  to  buy  goods  must 
be  adjusted  to  the  prices  of  goods)  would  have  to  be 
increased  in  that  ratio  in  order  to  secure  merely  the 
same  goods  as  before.  But  enterprisers,  wishing  to 
profit  by  the  lag  in  interest,  would  extend  the  loans 
beyond  this  old  or  original  point.  Therefore,  deposits 
based  on  loans  would  increase  in  a  greater  ratio.  That 
is,  the  ratio  M'  to  M  would  increase.  In  other  words, 
during  the  period  while  M  is  increasing,  M'  increases 
still  faster,  thus  disturbing  the  normal  ratio  between 
these  two  forms  of  currency. 

This,  however,  is  not  the  only  disturbance  caused  by 
the  increase  in  M.  There  are  disturbances  in  the  Q's  (or 
in  other  words  T)  in  V,  and  in  V.  These  will  be  taken 
up  in  order.  Trade  (the  Q's)  will  be  stimulated  by  the 
easy  terms  for  loans.  This  effect  is  always  observed 
during  rising  prices,  and  people  note  approvingl}^  that 
''business  is  good"  and  "times  are  booming."  Such 
statements  represent  the  point  of  view  of  the  ordinary 
business  man  who  is  an  "enterpriser-borrower."  They 
do  not  represent  the  sentiments  of  the  creditor,  the 
salaried  man,  or  the  laborer,  most  of  whom  are  silent  but 


62  THE    PURCHASING   POWER   OF   MONEY     [Chap.  IV 

long-suffering,  —  paying  higher  prices,  but  not  getting 
proportionally  higher  incomes. 

,      The  first  cause  of  the  unhealthy  increase  in  trade  lies 
/  K  in  the  fact  that  prices,  like  interest,  lag  behind  their 

'  full  adjustment  and  have  to  be  pushed  up,  so  to  speak, 
by  increased  purchases.  This  is  especially  true  in  cases 
where  the  original  impetus  came  from  an  increase  in 
money.  The  surplus  money  is  first  expended  at  nearly 
the  old  price  level,  but  its  continued  expenditure  grad- 
ually raises  prices.  In  the  meantime  the  volume  of 
purchases  will  be  somewhat  greater  than  it  would  have 
been  had  prices  risen  more  promptly.  In  fact,  from  the 
point  of  view  of  those  who  are  selling  goods,  it  is  the 
possibility  of  a  greater  volume  of  sales  at  the  old  prices 
which  gives  encouragement  to  an  increase  of  prices. 
Seeing  that  they  can  find  purchasers  for  more  goods 
than  before  at  the  previously  prevailing  prices,  or  for  as 
many  goods  as  before  at  higher  prices,  they  will  charge 
these  higher  prices. 

But  the  amount  of  trade  is  dependent,  almost  en- 
tirely, on  other  things  than  the  quantity  of  currency, 
so  that  an  increase  of  currency  cannot,  even  temporarily, 
very  greatly  increase  trade.  In  ordinarily  good  times 
practically  the  whole  community  is  engaged  in  labor,  pro- 
ducing, transporting,  and  exchanging  goods.  The  in- 
crease of  currency  of  a  "boom"  period  cannot,  of  itself, 
increase  the  population,  extend  invention,  or  increase 
the  efficiency  of  labor.  These  factors  pretty  definitely 
limit  the  amount  of  trade  which  can  be  reasonably 
carried  on.  So,  although  the  gains  of  the  enterpriser- 
borrower  may  exert  a  psychological  stimulus  on  trade, 
though  a  few  unemployed  may  be  employed,  and  some 
others  in  a  few  lines  induced  to  work  overtime,  and  al- 
though there  may  be  some  additional  buying  and  selling 


Sec.  3]  TEANSITION   PERIODS  63 

which  is  speculative,  yet  almost  the  entire  effect  of  an 
increase  of  deposits  must  be  seen  in  a  change  of 
prices.  Normally  the  entire  effect  would  so  express 
itself,  but  transitionally  there  will  be  also  some  increase 
in  the  Q's. 

We  next  observe  that  the  rise  in  prices  —  fall  in 
the  purchasing  power  of  money  —  will  accelerate  the  y^ 
circulation  of  money.  We  all  hasten  to  get  rid  of  any 
commodity  which,  like  ripe  fruit,  is  spoiling  on  our 
hands. ^  Money  is  no  exception;  when  it  is  depreciat- 
ing, holders  will  get  rid  of  it  as  fast  as  possible.  As 
they  view  it,  their  motive  is  to  buy  goods  which  appre- 
ciate in  terms  of  money  in  order  to  profit  by  the  rise  in 
their  value.  The  inevitable  result  is  that  these  goods  «x 
rise  in  price  still  further.  The  series  of  changes,  then, 
initiated  by  rising  prices,  expressed  more  fully  than 
before,  is  as  follows  :  —  "^ 

1.  Prices  rise. 

2.  Velocities  of  circulation  (F  and  V)  increase; 
the  rate  of  interest  rises,  but  not  sufficiently. 

3.  Profits  increase,  loans  expand,  and  the  Q's  in- 
crease. 

4.  Deposit  currency  {M')  expands  relatively  to 
money  (M). 

5.  Prices  continue  to  rise;  that  is,  phenomenon 
No.  1  is  repeated.     Then  No.  2  is  repeated,  and  so  on.     ^ 

It  will  be  noticed  that  these  changes  now  involve  all 

*  For  statistical  proof,  see  Pierre  des  Essars,  Journal  de  la  SociitS 
de  Statistique  de  Paris,  April,  1895,  p.  143.  The  figures  relate  only 
to  velocity  of  bank  deposits.  No  corresponding  figures  for  velocity 
of  circulation  of  money  exist.  Pierre  des  Essars  has  shown  that 
in  European  banks  V  reaches  a  maximum  in  crisis  years  almost 
without  fail.  The  same  I  find  true  in  this  country  as  shown  by 
the  ratio  of  clearings  to  deposits  in  New  York,  Boston,  and  Phila- 
delphia. 


64  THE    PURCHASING    POWER   OF   MONEY     [Chap.  IV 

the  magnitudes  in  the  equation  of  exchange.  They  are 
temporary  changes,  pertaining  only  to  the  transition 
period.  They  are  Hke  temporary  increases  in  power  and 
readjustments  in  an  automobile  climbing  a  hill. 

§  4 
Evidently  the  expansion  coming  from  this  cycle  of 
/  causes  cannot  proceed  forever.  It  must  ultimately 
spend  itself.  The  check  upon  its  continued  operation 
lies  in  the  rate  of  interest.  It  was  the  tardiness  of  the 
rise  in  interest  that  was  responsible  for  the  abnormal 
condition.  But  the  rise  in  interest,  though  belated,  is 
progressive,  and,  as  soon  as  it  overtakes  the  rate  of 
rise  in  prices,  the  whole  situation  is  changed.  If  prices 
are  rising  at  the  rate  of  2  per  cent  per  annum,  the  boom 
will  continue  only  until  interest  becomes  2  per  cent 
higher.  It  then  offsets  the  rate  of  rise  in  prices.  The 
banks  are  forced  in  self-defense  to  raise  interest  be- 
cause they  cannot  stand  so  abnormal  an  expansion 
of  loans  relatively  to  reserves.  As  soon  as  the  interest 
rate  becomes  adjusted,  borrowers  can  no  longer  hope 
to  make  great  profits,  and  the  demand  for  loans  ceases 
to  expand. 

There  are  also  other  forces  placing  a  limitation  on 
i\  further  expansion  of  deposit  currency  and  introducing 
a  tendency  to  contraction.  Not  only  is  the  amount 
of  deposit  currency  limited  both  by  law  and  by  prudence 
to  a  certain  maximum  multiple  of  the  amount  of  bank 
reserves ;  but  bank  reserves  are  themselves  limited  by 
the  amount  of  money  available  for  use  as  reserves. 
Further,  with  the  rise  of  interest,  the  value  of  certain 
collateral  securities,  such  as  bonds,  on  the  basis  of 
which  loans  are  made,  begins  to  fall.  Such  securities, 
being  worth  the  discounted  value  ofj  fixed  sums,  fall 


Sec.  4]  TRANSITION   PERIODS  65 

as  interest  rises ;  and  therefore  they  cannot  be  used  as 
collateral  for  loans  as  large  as  before.  This  check  to 
loans  is,  as  previously  explained,  a  check  to  deposits 
also. 

With  the  rise  of  interest,  those  who  have  counted 
on  renewing  their  loans  at  the  former  rates  and  for  the 
former  amounts  are  unable  to  do  so.  It  follows  that 
some  of  them  are  destined  to  fail.  The  failure  (or 
prospect  of  failure)  of  firms  that  have  borrowed  heavily 
from  banks  induces  fear  on  the  part  of  many  depositors 
that  the  banks  will  not  be  able  to  realize  on  these  loans. 
Hence  the  banks  themselves  fall  under  suspicion,  and  for 
this  reason  depositors  demand  cash.  Then  occur  ''runs 
on  the  banks,"  which  deplete  the  bank  reserves  at  the 
very  moment  they  are  most  needed.^  Being  short  of 
reserves,  the  banks  have  to  curtail  their  loans.  It  is 
then  that  the  rate  of  interest  rises  to  a  panic  figure. 
Those  enterprisers  who  are  caught  must  have  currency  ^ 
to  liquidate  their  obligations,  and  to  get  it  are  willing 
to  pay  high  interest.  Some  of  them  are  destined  to 
become  bankrupt,  and,  with  their  failure,  the  demand 
for  loans  is  correspondingly  reduced.  This  culmination 
of  an  upward  price  movement  is  what  is  called  a  crisis,^ —  ' 
a  condition  characterized  by  bankruptcies,  and  the  bank- 

*  A  part  of  the  theory  of  crises  here  presented  is  similarly  ex- 
plained in  a  paper  by  Harry  G.  Brown,  Yale  Review,  August,  1910, 
entitled  "Typical  Commeroial  Crises  versus  a  Money  Panic." 

2  Irving  Fisher,  Rate  of  Interest,  pp.  325,  326. 

^  This  is  the  definition  of  a  crisis  given  by  Juglar  and  the  his- 
tory of  crises  which  he  gives  in  detail  corresponds  to  the  descrip- 
tion. See  Juglar,  Des  Crises  Commerciales  et  de  leur  retour 
periodique  en  France  en  Angleterre  et  aux  Etats-Unis.  2d  ed., 
Paris  (Guillaumin),  1889,  pp.  4  and  5.  See  also  translation  of  part 
dealing  with  the  United  States,  by  De  Courcey  W.  Thom,  A  Brie} 
History  of  Panics  in  the  United  States,  New  York  (Putnam),  1893, 
pp.  7-10. 

¥ 


66  THE   PURCHASING   POWER  OF  MONEY     [Chap.  IV 

ruptcies  being  due  to  a  lack  of  cash  when  it  is  most 
needed. 

It  is  generally  recognized  that  the  collapse  of  bank 
credit  brought  about  by  loss  of  confidence  is  the  essential 
fact  of  every  crisis,  be  the  cause  of  the  loss  of  confidence 
what  it  may.  What  is  not  generally  recognized,  and 
what  it  is  desired  in  this  chapter  to  emphasize,  is  that 
this  loss  of  confidence  (in  the  typical  commercial  crisis 
here  described)  is  a  consequence  of  a  belated  adjustment 
in  the  interest  rate. 

It  is  not  our  purpose  here  to  discuss  nonmonetary 
causes  of  crises,  further  than  to  say  that  the  monetary 
/  causes  are  the  most  important  when  taken  in  connection 
with  the  maladjustments  in  the  rate  of  interest.  The 
other  factors  often  emphasized  are  merely  effects  of 
this  maladjustment.  " Overconsumption "  and  ''over- 
investment ' '  are  cases  in  point .  The  reason  many  people 
spend  more  than  they  can  afford  is  that  they  are  relying 
on  the  dollar  as  a  stable  unit  when  as  a  matter  of  fact 
its  purchasing  power  is  rapidly  falling.  The  bond- 
holder, for  instance,  is  beguiled  into  trenching  on  his 
capital.  He  never  dreams  that  he  ought  to  lay  by  a 
sinking  fund  because  the  decrease  in  purchasing  power 
of  money  is  reducing  the  real  value  of  his  principal. 
Again,  the  stockholder  and  enterpriser  generally  are 
beguiled  by  a  vain  reliance  on  the  stability  of  the  rate 
of  interest,  and  so  they  overinvest.  It  is  true  that  for 
a  time  they  are  gaining  what  the  bondholder  is  losing 
and  are  therefore  justified  in  both  spending  and  in- 
vesting more  than  if  prices  were  not  rising ;  and  at 
first  they  prosper.  But  sooner  or  later  the  rate  of 
interest  rises  above  what  they  had  reckoned  on,  and  they 
awake  to  the  fact  that  they  have  embarked  on  enterprises 
which  cannot  pay  these  high  rates. 


3ec.  5]  TRANSITION    PERIODS  67 

Then  a  curious  thing  happens :  borrowers,  unable 
to  get  easy  loans,  blame  the  high  rate  of  interest  for 
conditions  which  were  really  due  to  the  fact  that  the 
previous  rate  of  interest  was  not  high  enough.  Had 
the  previous  rate  been  high  enough,  the  borrowers 
never  would  have  overinvested. 

§5 

The  contraction  of  loans  and  deposits  is  accompanied 
by  a  decrease  in  velocities,  and  these  conspire  to  pre- 
vent a  further  rise  of  prices  and  tend  toward  a  fall. 
The  crest  of  the  wave  is  reached  and  a  reaction  sets  in. 
Since  prices  have  stopped  rising,  the  rate  of  interest, 
which  has  risen  to  compensate  the  rise  of  prices,  should 
fall  again.  But  just  as  at  first  it  was  slow  to  rise,  so 
now  it  is  slow  to  fall.  In  fact,  it  tends  for  a  time  to 
rise  still  further. 

The  mistakes  of  the  past  of  overborrowing  compel 
the  unfortunate  victims  of  these  mistakes  to  borrow 
still  further  to  protect  their  solvency.  It  is  this  special 
abnormality  which  marks  the  period  as  a  ''crisis." 
Loans  are  wanted  to  continue  old  debts  or  to  pay  these 
debts  by  creating  new  ones.  They  are  not  wanted 
because  of  new  investments  but  because  of  obligations 
connected  with  old  (and  ill-fated)  investments.  The 
problem  is  how  to  get  extricated  from  the  meshes  of 
past  commitments.  It  is  the  problem  of  liquidation. 
Even  when  interest  begins  to  fall,  it  falls  slowly,  and 
failures  continue  to  occur.  Borrowers  now  find  that 
interest,  though  nominally  low,  is  still  hard  to  meet. 
Especially  do  they  find  this  true  in  the  case  of  contracts 
made  just  before  prices  ceased  rising  or  just  before  they 
began  to  fall.  The  rate  of  interest  in  these  cases  is 
agreed  upon  before  the  change  in  conditions  takes  place. 


68  THE    PURCHASING    POWER   OF   MONEY     [Chap.  IV 

There  will,  in  consequence,  be  little  if  any  adjustment 
in  lowering  nominal  interest.  Because  interest  is  hard 
to  pay,  failures  continue  to  occur.  There  comes  to  be 
a  greater  hesitation  in  lending  on  any  but  the  best 
security,  and  a  hesitation  to  borrow  save  when  the 
prospects  of  success  are  the  greatest.  Bank  loans  tend 
to  be  low,  and  consequently  deposits  {M')  are  reduced. 
The  contraction  of  deposit  currency  makes  prices  fall 
still  more.  Those  who  have  borrowed  for  the  purpose 
of  buying  stocks  of  goods  now  find  they  cannot  sell 
them  for  enough  even  to  pay  back  what  they  have 
borrowed.  Owing  to  this  tardiness  of  the  interest  rate 
in  falling  to  a  lower  and  a  normal  level,  the  sequence 
of  events  is  now  the  opposite  of  what  it  was  before :  — 

1.  Prices  fall. 

2.  The  rate  of  interest  falls,  but  not  sufficiently. 

3 .  Enterpriser-borrowers,  discouraged  by  small  profits, 
contract  their  borrowings. 

4.  Deposit  currency  {M')  contracts  relatively  to 
money  (M). 

5.  Prices  continue  to  fall;  that  is,  phenomenon 
No.  1  is  repeated.    Then  No.  2  is  repeated,  and  so  on. 

Thus  a  fall  of  prices  generates  a  further  fall  of  prices. 
The  cycle  evidently  repeats  itself  as  long  as  the  rate 
of  interest  lags  behind.  The  man  who  loses  most  is 
the  business  man  in  debt.  He  is  the  typical  business 
man,  and  he  now  complains  that  ''business  is  bad." 
There  is  a  "depression  of  trade." 

During  this  depression,  velocities  (V  and  V)  are 
abnormally  low.  People  are  less  hasty  to  spend  money 
or  checks  when  the  dollars  they  represent  are  rising 
in  purchasing  power.  The  Q's  (or  quantities  in  trade) 
decline  because  (1)  the  initiators  of  trade  —  the  enter- 
priser-borrowers —  are  discouraged ;  (2)  the  inertia  of 


Sec.  5]  TRANSITION   PERIODS  69 

high  prices  can  be  overcome  only  by  a  falling  off  of 
expenditures ;  (3)  trade  against  money  which  alone  the 
Q's  represent  gives  way  somewhat  to  barter.  For  a 
time  there  is  not  enough  money  to  do  the  business 
which  has  to  be  done  at  existing  prices,  for  these  prices 
are  still  high  and  will  not  immediately  adjust  them- 
selves to  the  sudden  contraction.  When  such  a  ' '  money 
famine"  exists,  there  is  no  way  of  doing  all  the  business 
except  by  eking  out  money  transactions  with  barter. 
But  while  recourse  to  barter  eases  the  first  fall  of  prices, 
the  inconvenience  of  barter  immediately  begins  to 
operate  as  an  additional  force  tending  to  reduce  prices 
by  inducing  sellers  to  sell  at  a  sacrifice  if  only  money 
can  be  secured  and  barter  avoided ;  although  this  ef- 
fect is  partly  neutralized  for  a  time  by  a  decrease  in 
the  amount  of  business  which  people  will  attempt 
under  such  adverse  conditions.  A  statement  includ- 
ing these  factors  is :  — 

1.  Prices  fall. 

2.  Velocities  of  circulation  (F  and  V)  fall;  the  rate 
of  interest  falls,  but  not  sufficiently. 

3.  Profits  decrease;  loans  and  the  Q's  decrease. 

4.  Deposit  currency  (M')  contracts  relatively  to 
money  (M). 

Prices  continue  to  fall ;  that  is,  phenomenon  No.  1 
is  repeated.     Then  No.  2  is  repeated,  and  so  on. 

The  contraction  brought  about  by  this  cycle  of  causes 
becomes  self-Hmiting  as  soon  as  the  rate  of  interest 
overtakes  the  rate  of  fall  in  prices.  After  a  time, 
normal  conditions  begin  to  return.  The  weakest 
producers  have  been  forced  out,  or  have  at  least  been 
prevented  from  expanding  their  business  by  increased 
loans.  The  strongest  firms  are  left  to  build  up  a  new 
credit   structure.     The   continuous   fall   of  prices  has 


70  THE   PURCHASING   POWER   OP  .VIONEY     [Chap.  IV 

made  it  impossible  for  most  borrowers  to  pay  the  old 
high  rates  of  interest ;  the  demand  for  loans  diminishes, 
and  interest  falls  to  a  point  such  that  borrowers  can 
at  last  pay  it.  Borrowers  again  become  willing  to  take 
ventures ;  failures  decrease  in  number ;  bank  loans 
cease  to  decrease;  prices  cease  to  fall;  borrowing 
and  carrying  on  business  become  profitable ;  loans  are 
again  demanded ;  prices  again  begin  to  rise,  and  there 
occurs  a  repetition  of  the  upward  movement  already 
described. 

We  have  considered  the  rise,  culmination,  fall,  and 
recovery  of  prices.  These  changes  are  abnormal 
oscillations,  due  to  some  initial  disturbance.  The  up- 
ward and  downward  movements  taken  together  con- 
stitute a  complete  credit  cycle,  which  resembles  the 
forward  and  backward  movements  of  a  pendulum.^ 
In  most  cases  the  time  occupied  by  the  swing  of  the 
commercial  pendulum  to  and  fro  is  about  ten  years. 
While  the  pendulum  is  continually  seeking  a  stable 
position,  practically  there  is  almost  always  some  oc- 
currence to  prevent  perfect  equilibrium.  Oscillations 
are  set  up  which,  though  tending  to  be  self-corrective, 
are  continually  perpetuated  by  fresh  disturbances. 
\  Any  cause  which  disturbs  equilibrium  will  suffice  to 
I  set  up  oscillations.  One  of  the  most  common  of  such 
causes  is  an  increase  in  the  quantity  of  money. ^  An- 
other is  a  shock  to  business  confidence  (affecting  enter- 
prise, loans,  and  deposits).  A  third  is  short  crops, 
affecting  the  Q's.     A  fourth  is  invention. 

The  factors  in  the  equation  of  exchange  are  there- 

'  For  a  mathematical  treatment  of  this  analogy,  see  Pareto, 
Cours  d'Sconomie  politique,  Lausanne,  1897,  pp.  282-284. 

*  Such  would  seem  to  be  the  explanation  of  the  panic  of  1907. 
Cf.  Irving  Fisher,  Rate  of  Interest,  p.  336. 


Sec.  5]  TRANSITION   PERIODS  71 

fore  continually  seeking  normal  adjustment.  A  ship 
in  a  calm  sea  will  ''pitch"  only  a  few  times  before 
coming  to  rest,  but  in  a  high  sea  the  pitching  never 
ceases.  While  continually  seeking  equiUbrium,  the 
ship  continually  encounters  causes  which  accentuate 
the  oscillation.  The  factors  seeking  mutual  adjustment 
are  money  in  circulation,  deposits,  their  velocities,  the 
Q's  and  the  p's.  These  magnitudes  must  always  be 
linked  together  by  the  equation  MV  +  M'V  =  2pQ. 
This  represents  the  mechanism  of  exchange.  But  in 
order  to  conform  to  such  a  relation  the  displacement 
of  any  one  part  of  the  mechanism  spreads  its  effects 
during  the  transition  period  over  all  parts.  Since 
periods  of  transition  are  the  rule  and  those  of  equi- 
librium the  exception,  the  mechanism  of  exchange  is 
almost  always  in  a  dynamic  rather  than  a  static  con- 
dition. 

It  must  not  be  assumed  that  every  credit  cycle  is  so 
marked  as  to  produce  artificially  excessive  business  ac- 
tivity at  one  time  and  "hard  times"  at  another.  The 
rhythm  may  be  more  or  less  extreme  in  the  width  of  its 
fluctuations.  If  banks  are  conservative  in  making  loans 
during  the  periods  of  rising  prices,  and  the  expansion  of 
credit  currency  is  therefore  limited,  the  rise  of  prices  is 
likewise  limited,  and  the  succeeding  fall  is  apt  to  be  less 
and  to  take  place  more  gradually.  If  there  were  a  bet- 
ter appreciation  of  the  meaning  of  changes  in  the  price 
level  and  an  endeavor  to  balance  these  changes  by  ad- 
justment in  the  rate  of  interest,  the  oscillations  might 
be  very  greatly  mitigated.  It  is  the  lagging  behind 
of  the  rate  of  interest  which  allows  the  oscillations  to 
reach  so  great  proportions.  On  this  point  Marshall 
well  says :  "  The  cause  of  alternating  periods  of  in- 
flation and  depression  of  commercial  activity  ...  is 


72  THE    PURCHASING    POWER  OF  MONEY     [Chap.  IV 

intimately  connected  with  those  variations  in  the  real 
rate  of  interest  which  are  caused  by  changes  in  the 
purchasing  power  of  money.  For  when  prices  are 
likely  to  rise,  people  rush  to  borrow  money  and  buy 
goods,  and  thus  help  prices  to  rise ;  business  is  inflated, 
and  is  managed  recklessly  and  wastefully ;  those  working 
on  borrowed  capital  pay  back  less  real  value  than  they 
borrowed,  and  enrich  themselves  at  the  expense  of 
the  community.  When  afterwards  credit  is  shaken 
and  prices  begin  to  fall,  every  one  wants  to  get  rid  of 
commodities  which  are  falling  in  value  and  to  get  hold 
of  money  which  is  rapidly  rising;  this  makes  prices 
fall  all  the  faster,  and  the  further  fall  makes  credit 
shrink  even  more,  and  thus  for  a  long  time  prices  fall 
because  prices  have  fallen."  ^ 

A  somewhat  different  sort  of  cycle  is  the  seasonal 
fluctuation  which  occurs  annually.  Such  fluctuations, 
for  the  most  part,  are  due,  not  to  the  departure  from  a 
state  of  equilibrium,  but  rather  to  a  continuous  adjust- 
ment to  conditions,  which,  though  changing,  are  normal 
and  expected.  As  the  autumn  periods  of  harvesting  and 
crop  moving  approach,  there  is  a  tendency  toward  a 
lower  level  of  prices,  followed  after  the  passing  of  this 
period  and  the  approach  of  winter  by  a  rise  of  prices. 

§  6 

In  the  present  chapter  we  have  analyzed  the  phe- 
nomena characteristic  of  periods  of  transition.  We 
have  found  that  one  such  "boom"  period  leads  to  a 
reaction,  and  that  the  action  and  reaction  complete  a 
cycle  of  "prosperity"  and  "depression." 

It  has  been  seen  that  rising  prices  tend  towards  a 

^  Marshall,  Principles  of  Economics,  Sth  ed.,  London  (Macmillan), 
1907,  Vol.  I,  p.  594. 


Sec.  6]  TRANSITION    PERIODS  73 

higher  nominal  interest,  and  f  alUng  prices  tend  towards  a 
lower,  but  that  in  general  the  adjustment  is  incomplete. 
With  any  initial  rise  of  prices  comes  an  expansion  of  loans, 
owing  to  the  fact  that  interest  does  not  at  once  adjust 
itself.  This  produces  profits  for  the  enterpriser-bor- 
rower, and  his  demand  for  loans  further  extends  de- 
posit currency.  This  extension  still  further  raises 
prices,  a  result  accentuated  by  a  rise  in  velocities  though 
somewhat  mitigated  by  an  increase  in  trade.  When 
interest  has  become  adjusted  to  rising  prices,  and  loans 
and  deposits  have  reached  the  limit  set  for  them  by  the 
bank  reserves  and  other  conditions,  the  fact  that  prices 
no  longer  are  rising  necessitates  a  new  adjustment. 
Those  whose  business  has  been  unduly  extended  now 
find  the  high  rates  of  interest  oppressive.  Failures 
result,  constituting  a  commercial  crisis.  A  reaction  sets 
in ;  a  reverse  movement  is  initiated.  A  fall  of  prices, 
once  begun,  tends  to  be  accelerated  for  reasons  exactly 
corresponding  to  those  which  operate  in  the  opposite 
situation. 


CHAPTER  V 

INDIRECT   INFLUENCES   ON   PURCHASING   POWER 
§    1 

Thus  far  we  have  considered  the  level  of  prices  as 
affected  by  the  volume  of  trade,  by  the  velocities  of 
circulation  of  money  and  of  deposits,  and  by  the  quan- 
tities of  money  and  of  deposits.  These  are  the  only 
influences  which  can  directly  affect  the  level  of  prices. 
Any  other  influences  on  prices  must  act  through  these 
five.  There  are  myriads  of  such  influences  (outside  of 
the  equation  of  exchange)  that  affect  prices  through 
these  five.  It  is  our  purpose  in  this  chapter  to  note 
the  chief  among  them,  excepting  those  that  affect  the 
volume  of  money  {M) ;  the  latter  will  be  examined  in 
the  two  following  chapters. 

We  shall  first  consider  the  outside  influences  that 
affect  the  volume  of  trade  and,  through  it,  the  price 
level.  The  conditions  which  determine  the  extent  of 
trade  are  numerous  and  technical.  The  most  important 
may  be  classified  as  follows :  — 

1.  Conditions  affecting  producers. 

(a)  Geographical  differences  in  natural  resources. 
(6)   The  division  of  labor. 

(c)  Knowledge  of  the  technique  of  production. 

(d)  The  accumulation  of  capital. 

2.  Conditions  affecting  consumers. 

(a)  The  extent  and  variety  of  human  wants. 

74 


Sec.  1]  INDIRECT  INFLUENCES  75 

3.  Conditions  connecting  producers  and  consumers. 

(a)  Facilities  for  transportation. 

(b)  Relative  freedom  of  trade. 

(c)  Character  of  monetary  and  banking  systems. 

(d)  Business  confidence. 

1  (a).  It  is  evident  that  if  all  localities  were  exactly 
alike  in  their  natural  resources  and  in  their  compara- 
tive costs  of  production  little  or  no  trade  would  be  set 
up  between  them.  It  is  equally  true  that  the  greater 
the  difference  in  the  costs  of  production  of  different  arti- 
cles in  different  localities,  the  more  likely  is  there  to  be 
trade  between  them  and  the  greater  the  amount  of  that 
trade.  Primitive  trade  had  its  raison  d'etre  in  the  fact 
that  the  regions  of  this  earth  are  unlike  in  their  prod- 
ucts. The  traders  were  travelers  between  distant  coun- 
tries. Changes  in  commercial  geography  still  produce 
changes  in  the  distribution  and  volume  of  trade.  The 
exhaustion  of  gold  and  silver  mines  in  Nevada  and  of 
lumber  in  Michigan  have  tended  to  reduce  the  volume 
of  trade  of  these  regions,  both  external  and  internal. 
Contrariwise,  cattle  raising  in  Texas,  the  production  of 
coal  in  Pennsylvania,  of  oranges  in  Florida,  and  of  ap- 
ples in  Oregon  have  increased  the  volume  of  trade  for 
these  communities  respectively. 

1  (6).  Equally  obvious  is  the  influence  of  the  division 
of  labor.  Division  of  labor  is  based  in  part  on  differences 
in  comparative  costs  or  efforts  as  between  men,  —  cor- 
responding to  geographic  differences  as  between  coun- 
tries. These  two,  combined,  lead  to  local  differentia- 
tion of  labor,  making,  for  example,  the  town  of  Sheffield 
famous  for  cutlery,  Dresden  for  china,  Venice  for  glass, 
Paterson  for  silks,  and  Pittsburg  for  steel. 

1  (c).  Besides  local  and  personal  differentiation,  the 
state   of   knowledge   of  production  will   affect  trade. 


76  THE    PURCHASING   POWER  OF  MONEY       [Chap.  V 

The  mines  of  Africa  and  Australia  were  left  unworked 
for  centuries  by  ignorant  natives  but  were  opened  by 
white  men  possessing  a  knowledge  of  metallurgy.  Vast 
coal  fields  in  China  await  development,  largely  for  lack 
of  knowledge  of  how  to  extract  and  market  the  coal. 
Egypt  awaits  the  advent  of  scientific  agriculture,  to 
usher  in  trade  expansion.  Nowadays,  trade  schools 
in  Germany,  England,  and  the  United  States  are  in- 
creasing and  diffusing  knowledge  of  productive  tech- 
nique. 

1  (d).  But  knowledge,  to  be  of  use,  must  be  applied ; 
and  its  application  usually  requires  the  aid  of  capital. 
The  greater  and  the  more  productive  the  stock  or  capital 
in  any  community,  the  more  goods  it  can  put  into  the 
currents  of  trade.  A  mill  will  make  a  town  a  center 
of  trade.  Docks,  elevators,  warehouses  and  railway 
terminals  help  to  transform  a  harbor  into  a  port  of 
commerce. 

Since  increase  in  trade  tends  to  decrease  the  general 
level  of  prices,  anything  which  tends  to  increase  trade 
likewise  tends  to  decrease  the  general  level  of  prices. 
We  conclude,  therefore,  that  among  the  causes  tending 
to  decrease  prices  are  increasing  geographical  or  personal 
specialization,  improved  productive  technique,  and  the 
accumulation  of  capital.  The  history  of  commerce 
shows  that  all  these  causes  have  been  increasingly 
operative  during  a  long  period  including  the  last  century. 
Consequently,  there  has  been  a  constant  tendency,  from 
these  sources  at  least,  for  prices  to  fall. 

2  (a).  Turning  to  the  consumers'  side,  it  is  evident 
that  their  wants  change  from  time  to  time.  This  is 
true  even  of  so-called  natural  wants,  but  more  con- 
spicuously true  of  acquired  or  artificial  wants. 

Wants  are,  as  it  were,  the  mainsprings  of  economic 


Sec.  2]  INDIRECT  INFLUENCES  77 

activity  which  in  the  last  analysis  keep  the  economic 
world  in  motion.  The  desire  to  have  clothes  as  fine  as 
the  clothes  of  others,  or  finer,  or  different,  leads  to  the 
multiplicity  of  silks,  satins,  laces,  etc. ;  and  the  same 
principle  apphes  to  furniture,  amusements,  books,  works 
of  art,  and  every  other  means  of  gratification. 

The  increase  of  wants,  by  leading  to  an  increase  in 
trade,  tends  to  lower  the  price  level.  Historically, 
during  recent  times  through  invention,  education,  and 
the  emulation  coming  from  increased  contact  in  centers 
of  population,  there  has  been  a  great  intensification  and 
diversification  of  human  wants  and  therefore  increased 
trade.  Consequently,  there  has  been  from  these  causes 
a  tendency  of  prices  to  fall. 

§2 

3  (a).  Anything  which  facilitates  intercourse  tends 
to  increase  trade.  Anything  that  interferes  with  inter- 
course tends  to  decrease  trade.  First  of  all,  there  are 
the  mechanical  facilities  for  transport.  As  Macaulay 
said,  with  the  exception  of  the  alphabet  and  the  printing 
press,  no  set  of  inventions  has  tended  to  alter  civilization 
so  much  as  those  which  abridge  distance,  —  such  as 
the  railway,  the  steamship,  the  telephone,  the  tele- 
graph, and  that  conveyer  of  information  and  advertise- 
ments, the  newspaper.  These  all  tend,  therefore,  to 
decrease  prices. 

3  (b).  Trade  barriers  are  not  only  physical  but  legal. 
A  tariff  between  countries  has  the  same  influence  in 
decreasing  trade  as  a  chain  of  mountains.  The  freer 
the  trade,  the  more  of  it  there  will  be.  In  France, 
many  communities  have  a  local  tariff  (octroi)  which 
tends  to  interfere  with  local  trade.  In  the  United  States 
trade  is  free  within  the  country  itself,  but  between  the 


78  THE    PURCHASING    POWER   OF   MONEY       [Chap.  V 

United  States  and  other  countries  there  is  a  high  pro- 
tective tariff.  The  very  fact  of  increasing  faciUties 
for  transportation,  lowering  or  removing  physical 
barriers,  has  stimulated  nations  and  communities  to 
erect  legal  barriers  in  their  place.  Tariffs  not  only 
tend  to  decrease  the  frequency  of  exchanges,  but  to  the 
extent  that  they  prevent  international  or  interlocal 
division  of  labor  and  make  countries  more  alike  as  well 
as  less  productive,  they  also  tend  to  decrease  the 
amounts  of  goods  which  can  be  exchanged.  The  ulti- 
mate effect  is  thus  to  raise  prices. 

3  (c).  The  development  of  efficient  monetary  and 
banldng  systems  tends  to  increase  trade.  There  have 
been  times  in  the  history  of  the  world  when  money  was 
in  so  uncertain  a  state  that  people  hesitated  to  make 
many  trade  contracts  because  of  the  lack  of  knowledge 
of  what  would  be  required  of  them  when  the  contract 
should  be  fulfilled.  In  the  same  way,  when  people 
cannot  depend  on  the  good  faith  or  stability  of  banks, 
they  will  hesitate  to  use  deposits  and  checks. 

3  (d).  Confidence,  not  only  in  banks  in  particular, 
but  in  business  in  general,  is  truly  said  to  be  "the 
soul  of  trade."  Without  this  confidence  there  can- 
not be  a  great  volume  of  contracts.  Anything  that 
tends  to  increase  this  confidence  tends  to  increase 
trade.  In  South  America  there  are  many  places  wait- 
ing to  be  developed  simply  because  capitalists  do  not 
feel  any  security  in  contracts  there.  They  are  fearful 
that  by  hook  or  by  crook  the  fruit  of  any  investments 
they  may  make  will  be  taken  from  them. 

We  see,  then,  that  prices  will  tend  to  fall  through 
increase  in  trade,  which  may  in  turn  be  brought  about 
by  improved  transportation,  by  increased  freedom  of 
trade,  by  improved  monetary  and  banking  systems, 


Sec.  3]  INDIRECT   INFLUENCES  79 

and  by  business  confidence.  Historically,  during  recent 
years,  all  of  these  causes  have  tended  to  grow  in  power, 
except  freedom  of  trade.  Tariff  barriers,  however,  have 
only  partly  offset  the  removal  of  physical  barriers.  The 
net  effect  has  been  a  progressive  lowering  of  trade  re- 
strictions, and  therefore  the  tendency,  so  far  as  this 
group  of  causes  goes,  has  been  for  prices  to  fall. 

§3 

Having  examined  those  causes  outside  the  equation 
which  affect  the  volume  of  trade,  our  next  task  is  to 
consider  the  outside  causes  that  affect  the  velocities 
of  circulation  of  money  and  of  deposits.  For  the  most 
part,  the  causes  affecting  one  of  these  velocities  affect 
the  other  also.  These  causes  may  be  classified  as 
follows :  — 

1.  Habits  of  the  individual. 

(a)  As  to  thrift  and  hoarding. 

(6)  As  to  book  credit. 

(c)  As  to  the  use  of  checks. 

2.  Systems  of  payments  in  the  community. 

(a)  As  to  frequency  of  receipts  and  of  disburse- 
ments. 

(6)  As  to  regularity  of  receipts  and  disbursements. 

(c)  As  to  correspondence  between  times  and 
amounts  of  receipts  and  disbursements. 

3.  General  Causes. 

(a)  Density  of  population. 

(6)  Rapidity  of  transportation. 
1  (a).  Taking  these  up  in  order,  we  may  first  con- 
sider what  influence  thrift  has  on  the  velocity  of  cir- 
culation. Velocity  of  circulation  of  money  is  the  same 
thing  as  its  rate  of  turnover  It  is  found  by  dividing 
the  total  payments  effected  by  money  in  a  year  by  the 


80  THE    PURCHASING   POWER  OF  MONEY       [Chap.  V 

amount  of  money  in  circulation  in  that  year.  It  de- 
pends upon  the  rates  of  turnover  of  the  individuals 
who  compose  the  society.  This  velocity  of  circula- 
tion or  rapidity  of  turnover  of  money  is  the  greater 
for  each  individual  the  more  he  spends,  with  a  given 
average  amount  of  cash  on  hand;  or  the  less  average 
cash  he  keeps,  with  a  given  yearly  expenditure. 

The  velocity  of  circulation  of  a  spendthrift  may  be 
presumed  to  be  greater  than  the  average.^  He  is  al- 
ways apt  to  be  ''short"  of  funds,  —  to  have  a  small 
average  balance  on  hand.  But  his  thrifty  neighbor 
takes  care  to  provide  himself  with  cash  enough  to  meet 
all  contingencies.  The  latter  tends  to  hoard  and  lay 
by  his  money,  and  will,  therefore,  have  a  slower  velocity 
of  circulation.  When,  as  used  to  be  the  custom  in 
France,  people  put  money  away  in  stockings  and  kept 
it  there  for  months,  the  velocity  of  circulation  must 
have  been  extremely  slow.  The  same  principle  applies 
to  deposits.  In  a  certain  university  town  the  banks 
often  refuse  to  take  deposits  from  students  of  spend- 
ing habits  because  the  average  balances  of  the  latter 
are  so  low ;  or  insist  on  a  special  stipulation  that  the 
balance  shall  never  fall  below  $100. 

Hoarded  money  is  sometimes  said  to  be  withdrawn 
from  circulation.  But  this  is  only  another  way  of  say- 
ing that  hoarding  tends  to  decrease  the  velocity  of 
circulation. 

A  man  who  is  thrifty  is  usually,  to  some  extent,  a 
hoarder  either  of  money  ^  or  of  bank  deposits.  Laborers 
who   save   usually  keep  their  savings  in  the  form  of 

^  Cf .  Jevons,  Money  and  the  Mechanism  of  Exchange,  New  York 
(Appleton),  1896,  p.  336. 

^  Cf.  Harrison  H.  Brace,  Gold  Production  and  Future  Prices, 
New  York  (Bankers'  Publishing  Co.),  1910,  p.  122. 


Sec.  3]  INDIRECT   INFLUENCES  81 

money  until  enough  is  accumulated  to  be  deposited 
in  a  savings  bank.  Those  who  have  bank  accounts 
will  likewise  accumulate  considerable  deposits  when 
preparing  to  make  an  investment.  Banks  whose  de- 
positors are  "rapidly  making  money"  and  periodi- 
cally investing  the  same,  have,  it  is  said,  less  active 
accounts  than  banks  whose  depositors  ''live  up  to  their 
incomes." 

1  (6).  The  habit  of  "charging,"  i.e.  using  book 
credit,  tends  to  increase  the  velocity  of  circulation  of 
money,  because  the  man  who  gets  things  "charged" 
does  not  need  to  keep  on  hand  as  much  money  as  he 
would  if  he  made  all  payments  in  cash.  A  man  who 
pays  cash  daily  needs  to  keep  cash  for  daily  contin- 
gencies. The  system  of  cash  payments,  unlike  the 
system  of  book  credit,  requires  that  money  shall  be 
kept  on  hand  in  advance  of  purchases.  Evidently,  if 
money  must  be  provided  in  advance,  it  must  be  pro- 
vided in  larger  quantities  than  when  merely  required 
to  liquidate  past  debts.  This  is  true  for  two  reasons : 
First,  in  advance  of  purchases,  there  is  always  uncer- 
tainty as  to  when  money  will  be  needed  and  how  much, 
while  after  bills  are  incurred,  the  exact  sum  needed 
is  known.  Secondly,  and  as  a  consequence  of  the  first 
circumstance,  money  held  in  advance  must  be  held 
a  longer  time  than  money  received  after  a  use  for  it 
has  been  contracted  for.  In  short,  to  keep  money  in 
advance  requires  (a)  a  larger  margin  for  unforeseen 
contingencies  and  (6)  a  longer  period  before  being  dis- 
bursed during  which  the  money  is  idle.  In  the  system 
of  cash  payments,  a  man  must  keep  money  idle  in 
advance  lest  he  be  caught  in  the  embarrassing  position 
of  lacking  it  when  he  most  needs  it.  With  book  credit, 
he  knows  that  even  if  he  should  be  caught  without  a 


82  THE   PURCHASING   POWER  OP  MONEY       [Chap.  V 

cent  in  his  pocket,  he  can  still  get  supplies  on  credit. 
These  he  can  pay  for  when  money  comes  to  hand. 
Moreover,  this  money  need  not  lie  long  in  his  pocket. 
Immediately  it  is  received,  there  is  a  use  awaiting  it  to 
pay  debts  accumulated.  Now,  to  shorten  the  period 
of  waiting  evidently  decreases  the  average  balance 
carried,  even  if  in  the  end  the  same  sums  are  received 
and  disbursed.  For  instance,  a  laborer  receiving  and 
spending  $7  a  week,  if  he  cannot  ''charge,"  must  make 
his  week's  wages  last  through  the  week.  If  he  spends 
$1  a  day,  his  weekly  cycle  must  show  on  successive 
days  at  least  as  much  as  $7,  $6,  $5,  $4,  $3,  $2,  and 
$1,  at  which  time  another  $7  comes  in.  This  makes 
an  average  of  at  least  $4.  But  if  he  can  charge  every- 
thing and  then  wait  until  pay  day  to  meet  the  resulting 
obligations,  he  need  keep  nothing  through  the  week, 
paying  out  his  $7  when  it  comes  in.  His  weekly  cycle 
need  show  no  higher  balances  than  $7,  $0,  $0,  $0,  $0, 
$0,  $0,  the  average  of  which  is  only  SI. 

Through  book  credit,  therefore,  the  average  amount 
of  money  or  bank  deposits  which  each  person  must  keep 
at  hand  to  meet  a  given  expenditure  is  made  less.  This 
means  that  the  rate  of  turnover  is  increased ;  for  if 
people  spend  the  same  amounts  as  before,  but  keep 
smaller  amounts  on  hand,  the  quotient  of  the  amount 
spent  divided  by  the  amount  on  hand  must  increase. 

But  we  have  seen  that  to  increase  the  rate  of  turn- 
over will  tend  to  increase  the  price  level.  Therefore, 
book  credit  tends  to  increase  the  price  ^  level.  More- 
over, a  community  can  to  some  extent  cover  the  relative 
scarcity  of  money  of  a  period  when  business  is  large 

'  This  indirect  effect  on  the  price  level  must  not  be  confused  with 
the  direct  effect  sometimes  claimed.  See  §  1  of  Appendix  to  (this) 
Chapter  V. 


Sec.  4]  INDIRECT  INFLUENCES  83 

with  the  relative  surplus  of  a  period  when  fewer  de- 
mands are  made  on  its  supply  of  money.  Otherwise, 
to  maintain  the  same  general  level  of  prices,  there  would 
have  to  be  considerably  more  money  when  business 
was  large ;  and  this  money,  unless  it  were  some  form 
of  elastic  bank  currency  which  could  be  canceled  and 
retired,  would  lie  idle  during  those  seasons  when  busi- 
ness was  slack. 

In  short,  book  credit  economizes  money  (M)  even 
though  it  may  not  economize  money  payments  {E) 
and  therefore  increases  the  velocity  of  circulation 
of  money  {E/M). 

1  (c).  The  habit  of  using  checks  rather  than  money 
will  also  affect  the  velocity  of  circulation;  because  a 
depositor's  surplus  money  will  immediately  be  put 
into  the  bank  in  return  for  a  right  to  draw  by  check. 

Banks  thus  offer  an  outlet  for  any  surplus  pocket 
money  or  surplus  till  money,  and  tend  to  prevent 
the  existence  of  idle  hoards.  In  like  manner  surplus 
deposits  may  be  converted  into  cash  —  that  is,  ex- 
changed for  cash  —  as  desired.  In  short,  those  who 
make  use  both  of  cash  and  deposits  have  the  opportunity, 
by  adjusting  the  two,  to  prevent  either  from  being  idle. 

We  see,  then,  that  three  habits  —  spendthrift  habits, 
the  habit  of  charging,  and  the  habit  of  using  checks  — • 
all  tend  to  raise  the  level  of  prices  through  their  effects 
on  the  velocity  of  circulation  of  money,  or  of  deposits. 
It  is  believed  that  these  habits  (except  probably  the 
first)  have  been  increasing  rapidly  during  modern  times. 

§4 

2  (a).  The  more  frequently  money  or  checks  are 
received  and  disbursed,  the  shorter  is  the  average  in- 
terval between  the  receipt  and  the  expenditure  of  money 


84  THE    PURCHASING    POWER   OF   MONEY       [Chap.  V 

or  checks  and  the  more  rapid  is  the  velocity  of  circula- 
tion. 

This  may  best  be  seen  from  an  example.  A  change 
from  monthly  to  weekly  wage  payments  tends  to 
increase  the  velocity  of  circulation  of  money.  If  a 
laborer  is  paid  weekly  $7  and  reduces  this  evenly  each 
day,  ending  each  week  empty-handed,  his  average  cash, 
as  we  have  seen,  would  be  a  little  over  half  of  $7  or 
about  $4.  This  makes  his  turnover  nearly  twice  a 
week.  Under  monthly  payments  the  laborer  who 
receives  and  spends  an  average  of  $1  a  day  will  have 
to  spread  the  $30  more  or  less  evenly  over  the  follow- 
ing 30  days.  If,  at  the  next  pay  day,  he  comes  out 
empty-handed,  his  average  money  during  the  month 
has  been  about  $15.  This  makes  his  turnover  about 
twice  a  month.  Thus  the  rate  of  turnover  is  more 
rapid  under  weekly  than  under  monthly  payments. 

The  same  result  would  hold  if  we  assumed  that, 
instead  of  ending  the  cycle  empty-handed,  he  ended 
it  with  a  given  fraction  —  say  half  —  of  his  wages 
unspent.  Under  weekly  payments,  he  would  begin 
with  $10.50,  and  end  with  $3.50,  averaging  about  $7. 
Under  monthly  payments  he  would  thus  begin  with  an 
average  of  $45,  and  end  with  $15,  averaging  about  $30. 
In  the  former  case  his  average  velocity  of  circulation 
would  be  once  a  week  and  in  the  latter  once  a  month. 
The  turnover  will  thus  still  be  about  four  times  as 
rapid  under  weekly  as  under  monthly  payment. 
Thus  if  the  distribution  of  expenditure  over  the  two 
cycles  should  have  exactly  the  same  ''time  shape "^ 
(distribution   in    time),   weekly  payments   would    ac- 

^  Compare  Adolphe  Landry,  "La  Rapidite  de  la  Circulation 
Monetaire,"  Extrait  de  La  Revue  d' Economie  'politique,  Fevrier, 
1905. 


Sec.  4]  INDIRECT   INFLUENCES  85 

celerate  the  velocity  of  circulation  in  the  same  ratio 
which  a  month  bears  to  a  week.  As  a  matter  of  his- 
tory, however,  it  is  not  likely  that  the  substitution 
of  weekly  payments  for  monthly  payments  has  in- 
creased the  rapidity  of  circulation  of  money  among 
workingmen  fourfold,  because  the  change  in  another 
element,  book  credit,  would  be  likely  to  cause  a  some- 
what compensatory  decrease.  Book  credit  is  less 
likely  to  be  used  under  weekly  than  under  monthly 
payments.  Where  this  book-credit  habit  or  habit 
of  '^ charging"  is  prevalent,  the  great  bulk  of  money 
is  spent  on  pay  day.  It  is  probable  that  the  substitu- 
tion of  weekly  for  monthly  payments,  when  it  has 
taken  place,  has  enabled  many  workingmen,  who 
formerly  found  it  necessary  to  trade  on  credit,  to  make 
their  own  payments  in  cash,  thus  tendmg  to  decrease 
the  velocity  of  turnover  of  money. 

Frequency  of  disbursements  evidently  has  an  effect 
similar  to  the  effect  of  frequency  of  receipts ;  i.e.  it 
tends  to  accelerate  the  velocity  of  turnover,  or  cir- 
culation. 

2  (6).  Regularity  oi  payment  also  facilitates  the  turn- 
over. "When  the  workingman  can  be  fairly  certain 
of  both  his  receipts  and  expenditures,  he  can,  by  close 
calculation,  adjust  them  so  precisely  as  safely  to  end 
each  payment  cycle  with  an  empty  pocket.  This 
habit  is  extremely  common  among  certain  classes  of 
city  laborers.  On  the  other  hand,  if  the  receipts  and 
expenditures  are  irregular,  either  in  amount  or  in  time, 
prudence  requires  the  worker  to  keep  a  larger  sum  on 
hand,  to  insure  against  mishaps.^  Even  when  fore- 
known with  certainty,  irregular  receipts  require  a 
larger  average  sum  to  be  kept  on  hand.     This  state- 

*  Compare  Landry,  ibid. 


86  THE    PURCHASING    POWER   OF   MONEY       [Chap.  V 

merit  holds,  at  least,  if  we  assume  that  the  frequency 
of  payments  per  year  is  the  same  as  in  the  case  of 
regular  payments,  and  that  the  "tune  shape"  of  ex- 
penditures between  receipts  is  also  the  same.  Thus, 
suppose  that  a  workman  spends  at  the  rate  of  $1  a 
day  and  receives  at  the  average  rate  of  $1  a  day.  The 
average  amount  that  he  will  require  to  keep  on  hand 
will  be  less  if  his  receipts  occur  once  every  fortnight 
than  if  they  occur  at  intervals  of  three  weeks  and  one 
week  respectively  in  alternation.  For,  supposing  he 
tries  to  come  out  empty-handed  just  before  each  pay- 
ment, in  the  former  case  he  will  evidently  need  an  aver- 
age sum  each  fortnight  of  $7 ;  but  in  the  latter  case,  he 
will  need  for  the  first  period  of  three  weeks,  or  twenty- 
one  days,  $10.50,  and  in  the  second  period  $3.50, 
the  average  of  which  —  remembering  that  the  $10.50 
applies  for  three  weeks  and  the  $3.50  for  one  week  — 
will  be  $8.75.  We  may,  therefore,  conclude  that  reg- 
ularity, both  of  receipts  and  of  payments,  tends  to 
increase  velocity  of  circulation. 

2  (c).  Next,  consider  the  synchronizing  of  receipts 
and  disbursements,  i.e.  making  payments  at  the  same 
intervals  as  obtaining  receipts.  Where  payments  such 
as  rent,  interest,  insurance  and  taxes  occur  at  periods 
irrespective  of  the  times  of  receipts  of  money,  it  is 
often  necessary  to  accumulate  money  or  deposits  in 
advance,  thus  increasing  the  average  on  hand,  with- 
drawing money  from  use  for  a  time,  and  decreasing 
the  velocity  of  circulation.  This  result  may,  however, 
be  obviated  if  the  individual  is  willing  and  able  to 
borrow  in  order  to  meet  his  tax  or  other  special  ex- 
pense, repaying  the  loan  later  at  his  convenience. 
This  is  one  of  the  ways  in  which  banking,  as  already 
explained,  through  loans  and  deposits,  serves  the  con- 


Sec.  5]  INDIRECT  INFLUENCES  87 

venience  of  the  public  and  increases  the  velocity  of 
circulation  of  money  and  deposits.  Similarly  book 
credit  may  obviate  the  inconveniences  arising  from 
the  disharmony  between  the  times  of  receipt  and  dis- 
bursement; for  we  have  already  seen  that  it  is  a  great 
convenience  to  the  spender  of  money  or  of  deposits, 
if  dealers  to  whom  he  is  in  debt  will  allow  him  to 
postpone  payment  until  he  has  received  his  money 
or  his  bank  deposit.  This  arrangement  obviates  the 
necessity  of  keeping  much  money  or  deposits  on  hand, 
and  therefore  increases  their  velocity  of  circulation. 
We  conclude,  then,  that  synchronizing  and  regu- 
larity of  payment,  no  less  than  frequency  of  pa3nnent, 
have  tended  to  increase  prices  by  increasing  velocity 
of  circulation. 

§5 

3  (a).  The  more  densely  populated  a  locality,  the 
more  rapid  will  be  the  velocity  of  circulation.  ^ 

There  is  definite  evidence  that  this  is  true  of  bank 
deposits.  The  following  figures  ^  give  the  velocities  of 
circulation  of  deposits  in  ten  cities,  arranged  in  order 
of  size:  — 

Paris          116  Lisbon  29 

Berlin        161  Indianapolis        30 

Brussels     123  New  Haven         16 

Madrid       14  Athens  4 

Rome  43  Santa  Barbara      1 

Madrid  is  the  only  city  seriously  out  of  its  order  in 
respect  to  velocity  of  circulation. 

1  This  is  pointed  out  by  Kinley,  Money,  New  York  (Macmillan), 
1904,  p.  156. 

^  These  figures  are  the  medians  of  those  of  Pierre  des  Essars  for 
European  banks  (Journal  de  la  Societe  de  Statistique  de  Paris,  April, 
1895)  supplemented  by  data  secured  by  me  from  a  few  American 
banks. 


88  THE    PURCHASING    POWER   OF  MONEY       [Chap.  V 

3  (b).  Again,  the  more  extensive  and  the  speedier  the 
transportation  in  general,  the  more  rapid  the  circulation 
of  money.*  Anything  which  makes  it  easier  to  pass 
money  from  one  person  to  another  will  tend  to  increase 
the  velocity  of  circulation.  Railways  have  this  effect. 
The  telegraph  has  increased  the  velocity  of  circulation  of 
deposits,  since  these  can  now  be  transferred  thousands  of 
miles  in  a  few  minutes.  Mail  and  express,  by  facilitat- 
ing the  transmission  of  bank  deposits  and  money,  have 
likewise  tended  to  increase  their  velocity  of  circulation. 

We  conclude,  then,  that  density  of  population  and 
rapidity  of  transportation  have  tended  to  increase 
prices  by  increasing  velocities.  Historically  this  con- 
centration of  population  in  cities  has  been  an  im- 
portant factor  in  raising  prices  in  the  United  States. 

Ordinarily,  the  velocity  of  circulation  of  money  and 
the  velocity  of  circulation  of  deposits  will  be  similarly 
influenced  by  similar  causes.  In  time  of  panics, 
however,  if  the  confidence  of  depositors  is  shaken, 
the  tendency  is  for  deposits  to  be  withdrawn  while 
money  is  hoarded.  Hence,  for  a  time,  the  two  velocities 
may  change  in  opposite  directions,  although  there  are 
no  good  statistics  for  verifying  this  supposition. 

§6 

Lastly,  the  chief  specific  outside  influences  on  the 
volume  of  deposits  subject  to  check  are:  — 

(1)  The  system  of  banking  and  the  habits  of  the 
people  in  utilizing  that  system. 

(2)  The  habit  of  charging. 

1.  It  goes  without  saying  that  a  banking  system  must 

1  Cf.  Jevons,  Money  and  the  Mechanism  of  Exchange,  New  York 
(Appleton),  1896,  p.  336;  also  Kinley,  Money,  New  York  (Mao- 
miUan),  1904,  pp.  156  i  nd  157. 


Sec.  6]  INDIRECT   INFLUENCES  89 

be  devised  and  developed  before  it  can  be  used.  The 
invention  of  banking  has  made  deposit  currency  pos- 
sible, and  its  adoption  has  undoubtedly  led  to  a  great 
increase  in  deposits  and  consequent  rise  of  prices. 
Even  in  the  last  decade  the  extension  in  the  United 
States  of  deposit  banking  has  been  an  exceedingly 
powerful  influence  in  that  direction.  In  Europe  de- 
posit banking  is  still  in  its  infancy. 

2.  ''Charging"  is  often  a  preliminary  to  payment 
by  check,  rather  than  by  cash.  If  a  customer  did  not 
have  his  obligations  ''charged,"  he  would  pay  in  money 
and  not  by  check.  ^  The  ultimate  effect  of  this  practice, 
therefore,  is  to  increase  the  ratio  of  check  payments  to 
cash  payments  {E'  to  E)  and  the  ratio  of  deposits  to 
money  carried  {M'  to  M),  and  therefore  to  increase 
the  amount  of  credit  currency  which  a  given  quantity 
of  money  can  sustain. 

This  effect,  the  substitution  of  checks  for  cash  pay- 
ments, is  probably  by  far  the  most  important  effect 
of  "charging,"  and  exerts  a  powerful  influence  toward 
raising  prices. 

^  Andrew,  "  Credit  and  the  Value  of  Money."  Reprint  from  Papen 
and  Proceedings  of  the  Seventeenth  Annual  Meeting  American  Economic 
Association,  December,  1904,  p.  10. 


CHAPTER  VI 

INDIRECT  INFLUENCES  (continued) 


We  have  now  considered  those  influences  outside  the 
equation  of  exchange  which  affect  the  volume  of  trade 
(the  Q's),  the  velocities  of  circulation  of  money  and 
deposits  (V  and  V),  and  the  amount  of  deposits  (M'). 
We  have  reserved  for  separate  treatment  in  this  chapter 
and  the  following  the  outside  influences  that  affect  the 
quantity  of  money  (M). 

The  chief  of  these  may  be  classified  as  follows :  — 

1.  Influences  operating  through  the  exportation  and 
importation  of  money. 

2.  Influences  operating  through  the  melting  or  mint- 
ing of  money. 

3.  Influences  operating  through  the  production  and 
consumption  of  money  metals. 

4.  Influences  of  monetary  and  banking  systems,  to  be 
treated  in  the  next  chapter. 

The  first  to  be  considered  is  the  influence  of  foreign 
trade.  Hitherto  we  have  confined  our  studies  of  price 
levels  to  an  isolated  community,  having  no  trade  re- 
lation with  other  communities.  In  the  modern  world, 
however,  no  such  community  exists,  and  it  is  important 
to  observe  that  international  trade  gives  present-day 
problems  of  money  and  of  the  price  level  an  interna- 
tional character.  If  all  countries  had  their  irredeem- 
able paper  money,  and  had  no  money  acceptable 
elsewhere,  there  could  be  no  international  adjustment 

90 


Sec.  1]  INDIRECT  INFLUENCES   CONTINUED  91 

of  monetary  matters.  Price  levels  in  different  countries 
would  have  no  intimate  connection.  Indeed,  to  some 
extent  the  connection  is  actually  broken  between  exist- 
ing countries  which  have  different  metallic  standards, 
—  for  example,  between  a  gold-basis  and  a  silver-basis 
country,  —  although  through  their  nonmonetary  uses 
the  two  metals  are  still  somewhat  bound  together. 
But  where  two  or  more  nations  trading  with  each 
other  use  the  same  standard,  there  is  a  tendency  for  the 
price  levels  of  each  to  influence  profoundly  the  price 
levels  of  the  other. 

The  price  level  in  a  small  country  like  Switzerland 
depends  largely  upon  the  price  level  in  other  countries. 
Gold,  which  is  the  primary  or  full  weight  money  in 
most  civihzed  nations,  is  constantly  travelling  from  one 
country  or  community  to  another.  When  a  single 
small  country  is  under  consideration,  it  is  therefore 
preferable  to  say  that  the  quantity  of  money  in  that 
country  is  determined  by  the  universal  price  level, 
rather  than  to  say  that  its  level  of  prices  is  determined 
by  the  quantity  of  money  within  its  borders.  An 
individual  country  bears  the  same  relation  to  the  world 
that  a  lagoon  bears  to  the  ocean.  The  level  of  the 
ocean  depends,  of  course,  upon  the  quantity  of  water 
in  it.  But  when  we  speak  of  the  lagoon,  we  reverse  the 
statement,  and  say  that  the  quantity  of  water  in  it 
depends  upon  the  level  of  the  ocean.  As  the  tide  in 
the  outside  ocean  rises  and  falls,  the  quantity  of  water 
in  the  lagoon  will  adjust  itself  accordingly. 

To  simplify  the  problem  of  the  distribution  of  money 
among  different  communities,  we  shall,  for  the  time 
being,  ignore  the  fact  that  money  consists  ordinarily 
of  a  material  capable  of  nonmonetary  uses  and  may 
be  melted  or  minted. 


92  THE    PURCHASING   POWER   OF  MONEY     [Chap.  VI 

Let  US,  then,  consider  the  causes  that  determine  the 
quantity  of  money  in  a  state  hke  Connecticut.  If  the 
level  of  prices  in  Connecticut  temporarily  falls  below 
that  of  the  surrounding  states,  Rhode  Island,  Massa- 
chusetts, and  New  York,  the  effect  is  to  cause  an  export 
of  money  from  these  states  to  Connecticut,  because 
people  will  buy  goods  wherever  they  are  cheapest  and 
sell  them  wherever  they  are  dearest.  With  its  low 
prices,  Connecticut  becomes  a  good  place  to  buy  from, 
but  a  poor  place  to  sell  in.  But  if  outsiders  buy  of 
Connecticut,  they  will  have  to  bring  money  to  buy 
with.  There  will,  therefore,  be  a  tendency  for  money 
to  flow  to  Connecticut  until  the  level  of  prices  there 
rises  to  a  level  which  will  arrest  the  influx.  If,  on  the 
other  hand,  prices  in  Connecticut  are  higher  than  in 
surrounding  states,  it  becomes  a  good  place  to  sell  to  and 
a  poor  place  to  buy  from.  But  if  outsiders  sell  to  Con- 
necticut, they  will  receive  money  in  exchange.  There 
is  then  a  tendency  for  money  to  flow  out  of  Connecticut 
until  the  level  of  prices  in  Connecticut  is  lower. 

But  it  must  not  be  inferred  that  the  prices  of  various 
articles  or  even  the  general  level  of  prices  will  become 
precisely  the  same  in  different  countries.  Distance, 
ignorance  as  to  where  the  best  markets  are  to  be  found, 
tariffs,  and  costs  of  transportation  help  to  maintain 
price  differences.  The  native  products  of  each  region 
tend  to  be  cheaper  in  that  region.  They  are  exported 
as  long  as  the  excess  of  prices  abroad  is  enough  to  more 
than  cover  the  cost  of  transportation.  Practically,  a 
commodity  will  not  be  exported  at  a  price  which  would 
not  at  least  be  equal  to  the  price  in  the  country  of  origin, 
plus  the  freight.  Many  commodities  are  shipped  only 
one  way.  Thus,  wheat  is  shipped  from  the  United 
States  to  England,  but  not  from  England  to  the  United 


Sec.  1]  INDIRECi"   INFLUENCES   CONTINUED  93 

States.  It  tends  to  be  cheaper  in  the  United  States. 
Large  exportations  raise  its  price  in  America  toward  the 
price  in  England,  but  it  will  usually  keep  below  that 
price  by  the  cost  of  transportation.  Other  commodities 
that  are  cheap  to  transport  will  be  sent  in  either  direc- 
tion, according  to  market  conditions. 

But,  although  international  and  interlocal  trade  will 
never  bring  about  exact  uniformity  of  price  levels,  it 
will,  to  the  extent  that  it  exists,  produce  an  adjustment 
of  these  levels  toward  uniformity  by  regulating  in  the 
manner  already  described  the  distribution  of  money. 
If  one  commodity  enters  into  international  trade,  it 
alone  will  suffice,  though  slowly,  to  act  as  a  regulator 
of  money  distribution ;  for  in  return  for  that  com- 
modity, money  may  flow  and,  as  the  price  level  rises 
or  falls,  the  quantity  of  that  commodity  sold  may 
be  correspondingly  adjusted.  In  ordinary  intercourse 
between  nations,  even  when  a  deliberate  attempt  is 
made  to  interfere  with  it  by  protective  tariffs,  there 
will  always  be  a  large  number  of  commodities  thus 
acting  as  outlets  and  inlets.  And  since  the  quantity 
of  money  itself  affects  prices  for  all  sorts  of  commodi- 
ties, the  regulative  effect  of  international  trade  applies, 
not  simply  to  the  commodities  which  enter  into  that 
trade,  but  to  all  others  as  well.  It  follows  that  now- 
adays international  and  interlocal  trade  is  constantly 
regulating  price  levels  throughout  the  world. 

We  must  not  leave  this  subject  without  emphasizing 
the  effects  of  a  tariff  on  the  purchasing  power  of  money. 
When  a  country  adopts  a  tariff,  the  tendency  is  for  the 
level  of  prices  to  rise.  A  tariff  obviously  raises  the 
prices  of  the  ''protected"  goods.  But  it  does  more 
than  that,  —  it  tends  also  to  raise  the  prices  of  goods 
in   general.     Thus,   the   tariff  first  causes  a  decrease 


94  THE   PURCHASING    POWER   OF  MONEY     [Chap.  VI 

in  imports.  Though  in  the  long  run  this  decrease  in 
imports  will  lead  to  a  corresponding  decrease  in  exports, 
yet  at  first  there  will  be  no  such  adjustment.  The 
foreigner  will,  for  a  time,  continue  to  buy  from  the  pro- 
tected country  almost  as  much  as  before.  This  will 
result  temporarily  in  an  excess  of  that  country's  exports 
over  its  imports,  or  a  so-called  ''favorable"  balance  of 
trade,  and  a  consequent  inflow  of  money.  This  inflow 
will  eventually  raise  the  prices,  not  alone  of  protected 
goods,  but  of  other  goods  as  well.  The  rise  will  con- 
tinue till  it  reaches  a  point  high  enough  to  put  a  stop 
to  the  ''favorable"  balance  of  trade. 

Although  the  "favorable  balance"  of  trade  created 
by  a  tariff  is  temporary,  it  leaves  behind  a  permanent 
increase  of  money  and  of  prices.  The  tariff  wall  is  a 
sort  of  dam,  causing  an  elevation  in  the  prices  of  the 
goods  impounded  behind  it. 

This  fact  is  sometimes  overlooked  in  the  theory  of 
international  trade  as  commonly  set  forth.  Emphasis 
is  laid  instead  on  the  fact  that  in  the  last  analysis  the 
trade  is  of  goods  for  goods,  not  of  money  for  goods,  and 
that  a  tariff  on  imports  reduces,  not  only  imports,  but 
exports  also, —  that  it  merely  interrupts  temporarily  the 
virtual  barter  between  nations.  The  effect  of  a  tax  on 
imports  is  likened  to  that  of  a  tax  on  exports.  But  in 
respect  to  effects  on  price  levels  a  tax  on  imports  and  a 
tax  on  exports  are  diametrically  opposed.  If  we  place 
our  tax  on  exports,  we  first  interfere  with  exports.  The 
imports  are  not  checked  until  money  has  flowed  out 
and  has  reduced  the  general  price  level  enough  to  de- 
stroy the  "unfavorable"  balance  of  trade  first  created. 
We  conclude  that  the  general  purchasing  power  of 
money  is  reduced  by  a  tariff  and  that  it  would  be  in- 
creased by  a  tax  on  exports. 


Sec.  1]  INDIRECT  INFLUENCES   CONTINUED  95 

This  is,  perhaps,  the  chief  reason  why  a  protective 
tariff  seems  to  many  a  cause  of  prosperity.  It  furnishes 
a  temporary  stimulus,  not  only  to  protected  industries, 
but  to  trade  in  general,  which  is  really  simply  the  stimu- 
lus of  money  inflation. 

Our  present  interest  in  international  trade,  however, 
is  mainly  directed  to  its  effects  on  international  price 
levels.  Except  for  the  export  or  import  of  money  to 
adjust  the  price  levels,  international  trade  is  at  bottom 
merely  an  interchange  of  goods.  Where  the  price  level 
is  not  concerned,  the  money  value  of  the  goods  sold  by  a 
country  will  exactly  equal  the  value  of  those  bought. 
Only  when  there  is  a  difference  in  these  values,  or  a 
"balance  of  trade,"  will  there  be  any  flow  of  money 
and  consequently  any  tendency  to  modify  the  price 
level.^ 

We  have  shown  how  the  international  and  interlocal 
equilibrium  of  prices  may  be  disturbed  by  differential 
changes  in  the  quantity  of  money  alone.  It  may  also 
be  disturbed  by  differential  changes  in  the  volume 
of  bank  deposits ;  or  in  the  velocity  of  circulation  of 
money ;  or  in  the  velocity  of  circulation  of  bank  de- 
posits ;  or  in  the  volume  of  trade.  But  whatever  may 
be  the  source  of  the  difference  in  price  levels,  equilibrium 
will  eventually  be  restored  through  an  international  or 
interlocal  redistribution  of  money  and  goods  brought 
about  by  international  and  interlocal  trade.  Other 
elements  in  the  equation  of  exchange  than  money  and 
commodities  cannot  be  transported  from  one  place  to 
another. 

Except  for  transitional  effects,  then,  international 
differences  of  price  levels  produce  changes  only  in  one 

1  For  mathematical  statement,  see  §  1  of  Appendix  to  (this) 
Chapter  VI. 


96  THE    PURCHASING    POWER   OF   MONEY     [Chap.  VI 

of  the  elements  in  the  equation  of  exchange,  —  the 
volume  of  money.  Practically,  of  course,  transition 
periods  may  be  incessant  or  chronic.  It  seldom  happens 
that  a  nation  has  no  balance  of  trade.  For  decades  Ori- 
ental nations  took  silver  from  Occidental  nations  even 
when  silver  was,  under  the  bimetallic  regime,  at  a  stable 
ratio  with  gold.  In  Europe  there  was  a  consequent 
long-continued  tendency  for  prices  to  fall,  and  in  Asia 
a  tendency  to  rise,  with  all  the  other  transitional  effects 
involved. 

§2 

We  have  seen  how  M  in  the  equation  of  exchange 
is  affected  by  the  import  or  export  of  money.  Con- 
sidered with  reference  to  the  M  in  any  one  of  the  coun- 
tries concerned,  the  M's,  in  all  the  others  are  ''outside 
influences." 

Proceeding  now  one  step  farther,  we  must  consider 
those  influences  on  M  that  are  not  only  outside  of  the 
equation  of  exchange  for  a  particular  country,  but  out- 
side those  for  the  whole  world.  Besides  the  monetary 
inflow  and  outflow  through  import  and  export,  there 
is  an  inflow  and  outflow  through  minting  and  melting. 
In  other  words,  not  only  do  the  stocks  of  money  in  the 
world  connect  with  each  other  like  interconnecting 
bodies  of  water,  but  they  connect  in  the  same  way  with 
the  outside  stock  of  bullion.  In  the  modern  world  one 
of  the  precious  metals,  such  as  gold,  usually  plays  the 
part  of  primary  money,  and  this  metal  has  two  uses,  — 
a  monetary  use  and  a  commodity  use.  That  is  to  say, 
gold  is  not  only  a  money  material,  but  a  commodity  as 
well.  In  their  character  of  commodities,  the  precious 
metals  are  raw  materials  for  jewelry,  works  of  art,  and 
other  products  into  which  they  may  be  wrought.     It  is 


Sec.  2]  INDIRECT   INFLUENCES   CONTINUED  97 

in  this  unmanufactured  or  raw  state  that   they  are 
called  bullion. 

Gold  money  may  be  changed  into  gold  bullion,  and 
vice  versa.  In  fact,  both  changes  are  going  on  con- 
stantly, for  if  the  value  of  gold  as  compared  with  other 
commodities  is  greater  in  the  one  use  than  in  the  other, 
gold  will  immediately  flow  toward  whichever  use  is 
more  profitable,  and  the  market  price  of  gold  bullion 
will  determine  the  direction  of  the  flow.  Since  100 
ounces  of  gold,  y^  fine,  can  be  transformed  into  $1860, 
the  market  value  of  so  much  gold  bullion,  ^^  fine,  must 
tend  to  be  $1860.  If  it  costs  nothing  to  have  bullion 
coined  into  money,  and  nothing  to  melt  money  into 
bullion,  there  will  be  an  automatic  flux  and  reflux  from 
money  to  bullion  and  from  bullion  to  money  that  will 
prevent  the  price  of  bullion  from  varying  greatly.  On 
the  one  hand,  if  the  price  of  gold  bullion  is  greater  than 
the  money  which  could  be  minted  from  it,  no  matter 
how  slight  the  difference  may  be,  the  users  of  gold  who 
require  bullion  —  notably  jewelers  —  will  save  this 
difference  by  melting  gold  coin  into  bullion.  Con- 
trariwise, if  the  price  of  bullion  is  less  than  the  value 
of  gold  coin,  the  owners  of  bullion  will  save  the  differ- 
ence by  taking  bullion  to  the  mint  and  having  it  coined 
into  gold  dollars,  instead  of  selling  it  in  the  bullion 
market.  The  effect  of  melting  coin,  on  the  one  hand, 
is  to  decrease  the  amount  of  gold  money  and  increase 
the  amount  of  gold  bullion,  thereby  lowering  the  value 
of  gold  as  bullion  and  raising  the  value  of  gold  as  money; 
thereby  lowering  the  price  level  and  restoring  the  equal- 
ity between  bullion  and  money.  The  effect  of  minting 
bullion  into  coin  is,  by  the  opposite  process,  to  bring  the 
value  of  gold  as  coin  and  the  value  of  gold  as  bullion 
again   into   equilibrium.     In   practice,  the  balance   is 


98  THE    PURCHASING   POWER   OF  MONEY     [Chap.  VI 

probably  ^  maintained  chiefly  by  turning  newly  mined 
gold  into  the  one  or  the  other  use  according  to  the  mar- 
ket. By  thus  feeding  the  two  reservoirs  according  to 
their  respective  needs  there  is  saved  the  necessity  of  any 
great  amount  of  interflow  between  money  and  the  arts. 

Where  a  charge  —  called  "  seigniorage  "  —  is  made  for 
changing  bulhon  into  coin,  or  where  the  process  in- 
volves expense  or  delay,  the  flow  of  bullion  into  currency 
will  be  to  that  extent  impeded.  But  under  a  modern 
system  of  free  coinage  and  with  modern  methods  of 
metallurgy,  both  melting  and  minting  may  be  performed 
so  inexpensively  and  so  quickly  that  there  is  practically 
no  cost  or  delay  involved.  In  fact,  there  are  few  in- 
stances of  more  exact  price  adjustment  than  the  ad- 
justment between  gold  bullion  and  gold  coin.  It 
follows  that  the  quantity  of  money,  and  therefore  its 
purchasing  power,  is  directly  dependent  on  that  of  gold 
bullion. 

The  stability  of  the  price  of  gold  bullion  expressed  in 
gold  coin  causes  confusion  in  the  minds  of  many  people, 
giving  them  the  erroneous  impression  that  there  is  no 
change  in  the  value  of  money.  Indeed,  this  stability  has 
often  been  cited  to  show  that  gold  is  a  stable  standard 
of  value.  Dealers  in  objects  made  of  gold  seem  to 
misunderstand  the  significance  of  the  fact  that  an  ounce 
of  gold  always  costs  about  $18.60  in  the  United  States 
or  £3  17s.  10-2  <i.  i^i  England.  This  means  nothing 
more  than  the  fact  that  gold  in  one  form  and  meas- 
ured in  one  way  will  always  bear  a  constant  ratio  to 
gold  in  another  form  and  measured  in  another  way. 
An  ounce  of  gold  bullion  is  worth  a  fixed  number  of  gold 
dollars,  for  the  same  reason  that  a  pound  sterling  of 

1  Cf.  De  Launay,  The  World's  Gold,  New  York  (Putnam),  1908, 
pp.  179-183. 


Sec.  3]  INDIRECT   INFLUENCES   CONTINUED  99 

gold  is  worth  a  fixed  number  of  gold  dollars,  or  that  a 
gold  eagle  is  worth  a  fixed  number  of  gold  dollars. 

Except,  then,  for  extremely  slight  and  temporary- 
fluctuations,  gold  bullion  and  gold  money  must  always 
have  the  same  value.  Therefore,  in  the  following  dis- 
cussion respecting  the  more  considerable  fluctuations 
affecting  both,  we  shall  speak  of  these  values  inter- 
changeably as  'Hhe  value  of  gold." 

§  3 

The  stock  of  bullion  is  not  the  ultimate  outside 
influence  on  the  quantity  of  money.  As  the  stock  of 
bullion  and  the  stock  of  money  influence  each  other, 
so  the  total  stock  of  both  is  influenced  by  production 
and  consumption.  The  production  of  gold  consists  of 
the  output  of  the  mines,  which  constantly  tends  to  add 
to  the  existing  stocks  both  of  bullion  and  coin.  The 
consumption  of  gold  consists  of  the  use  of  bullion  in 
the  arts  by  being  wrought  up  into  jewelry,  gilding,  etc., 
and  of  losses  by  abrasion,  shipwreck,  etc.  If  we  con- 
sider the  amount  of  gold  coin  and  bullion  as  contained 
in  a  reservoir,  production  would  be  the  inflow  from 
the  mines,  and  consumption  the  outflow  to  the  arts 
and  by  destruction  and  loss.  To  the  inflow  from  the 
mines  should  be  added  the  reinflow  from  forms  of  art 
into  which  gold  had  previously  been  wrought,  but 
which  have  grown  obsolete.  This  is  illustrated  by 
the  business  of  producing  gold  bullion  by  burning 
gold  picture  frames. 

We  shall  consider  first  the  inflow  or  production, 
and  afterward  the  outflow  or  consumption.  The  reg- 
ulator of  the  inflow  (which  practically  means  the 
production  of  gold  from  the  mines)  is  its  estimated 
''marginal   cost   of  production." 


100  THE    PURCHASING    POWER   OF   MONEY     [Chap.  VI 

Mining  is  a  hazardous  business  and  estimates  are 
subject  to  great  error.  But  however  erroneous  the 
estimated  cost,  it  exerts  a  regulatory  power  over  pro- 
duction. Wherever  the  estimated  cost  of  producing 
a  dollar  of  gold  is  less  than  the  existing  value  of  a  dollar 
in  gold,  it  will  normally  be  produced.  Wherever  the 
cost  of  production  exceeds  the  existing  value  of  a  dollar, 
gold  will  normally  not  be  produced.  In  the  former 
case  the  production  of  gold  is  profitable ;  in  the  latter 
it  is  unprofitable.  There  will  be  an  intermediate  or 
neutral  point  at  which  normally  profitable  production 
ceases  and  unprofitable  production  begins,  a  point  at 
which  the  cost  of  producing  $100  will  be  exactly  $100. 
The  cost  at  this  point  is  called  the  marginal  cost  of 
production.  At  the  richest  mines,  the  cost  of  produc- 
tion is  extremely  small.  From  this  low  standard  the 
cost  gradually  rises  at  other  mines,  until  the  marginal 
mine  is  reached,  at  which  the  cost  will  normally  be 
equal  to  the  value  of  the  product.  In  fact,  there 
exists  a  marginal  point  of  production,  not  only  as 
among  different  mines,  but  for  each  mine  individually. 
The  fact  that  cost  tends  in  general  to  increase  with 
increased  product  is  due  to  the  fact  that  gold  is  an 
extractive  industry.  It  is  subject  to  the  law  of  increas- 
ing cost,  or,  as  it  is  often  expressed,  ''the  law  of  decreas- 
ing returns."  If  a  mine  is  only  moderately  worked,  the 
cost  of  production  per  ounce  of  gold  will  be  less  than 
if  it  is  worked  at  more  nearly  its  full  capacity,  and 
there  will  always  be  a  rate  of  working  such  that  the 
cost  per  ounce  of  any  extension  in  that  rate  of  working 
will  make  the  extension  barely  profitable.  It  will  pay 
to  extend  production  to  the  point  where  the  additional 
return  is  just  equal  to  the  consequent  additional  cost, 
but  no  further.     The  mine  operator  may  unintention- 


Sec.  3]  INDIRECT   INFLUENCES   CONTINUED  101 

ally  or  temporarily  overshoot  the  mark  or  fall  within 
it,  but  such  errors  will  only  stimulate  him  to  correct 
them;  and  gold  production  will  always  tend  toward 
an  equilibrium  in  which  the  marginal  cost  of  produc- 
tion will  (when  interest  is  added)  be  equal  to  the 
value  of  the  product. 

This  holds  true  in  whatever  way  cost  of  production 
is  measured,  whether  in  terms  of  gold  itself,  or  in 
terms  of  some  other  commodity  such  as  wheat,  or  of 
commodities  in  general,  or  of  any  supposed  ''absolute" 
standard  of  value.  In  gold-standard  countries  gold 
miners  do  actually  reckon  the  cost  of  producing  gold 
in  terms  of  gold.  From  their  standpoint  it  is  a  need- 
less complication  to  translate  the  cost  of  production 
and  the  value  of  the  product  into  some  other  standard 
than  gold.  They  are  interested  in  the  relation  between 
the  two,  and  this  relation  will  not  be  affected  by  the 
standard. 

To  translate  the  cost  and  value  from  gold  money 
into  wheat,  it  is  only  necessary  to  divide  both  cost 
and  value  by  the  price  of  wheat  in  gold  money. 
Such  a  change  in  the  method  of  expressing  both 
cost  and  value  will  not  affect  their  relation  to  each 
other. 

To  illustrate  how  the  producer  of  gold  measures 
everything  in  terms  of  gold,  suppose  that  the  price 
level  rises.  Assuming  that  the  rise  of  prices  applies 
to  wages,  machinery,  fuel,  and  the  other  expenses  of 
producing  gold,  he  will  then  have  to  pay  more  dollars 
for  wages,  machinery,  fuel,  etc.,  while  the  prices  ob- 
tained for  his  product  (expressed  in  those  same  dol- 
lars) will,  as  always,  remain  unchanged.  Conversely, 
a  fall  in  the  level  will  lower  his  cost  of  production 
(measured  in  dollars),  while  the  price  of  his  product 


102  THE    PURCHASING    POWER   OF   MONET    [Chap.  VI 

will  still  remain  the  same.^  Thus  we  have  a  constant 
number  expressing  the  price  of  gold  product  and  a 
variable  number  expressing  its  cost  of  production. 

If  we  express  the  same  phenomena,  not  in  terms  of 
gold,  but  in  terms  of  wheat,  or  rather,  let  us  say,  in 
terms  of  goods  in  general,  we  shall  have  the  opposite 
conditions.  When  prices  rise,  the  purchasing  power  of 
money  falls,  and  this  purchasing  power  is  the  value  of 
the  product  expressed  in  terms  of  goods  in  general. 
If  the  mining  costs  change  with  the  general  price  move- 
ment, there  will  not  occur  any  change  in  the  cost  of 
producing  gold  relatively  to  goods.  There  will,  however, 
be  a  change  in  the  value  of  the  gold  product.  That 
is,  we  shall  then  have  a  variable  number  expressing  the 
price  of  the  gold  product  and  a  constant  number  ex- 
pressing its  cost  of  production. 

Thus  the  comparison  between  price  and  cost  of 
production  is  the  same,  whether  we  use  gold  or  other 
commodities  as  our  criterion.  In  the  one  view  — 
i.e.  when  prices  are  measured  in  gold — a  rise  of  prices 
means  a  rise  in  the  gold  miner's  cost  of  production; 
in  the  other  view  —  i.e.  when  prices  are  measured 
in  other  goods  —  the  same  rise  in  prices  means  a  fall  in 
the  price  (purchasing  power)  of  his  product.  In  either 
view  he  will  be  discouraged.  He  will  look  at  his  troubles 
in  the  former  light,  i.e.  as  a  rise  in  the  cost  of  produc- 
tion ;  but  we  shall  find  it  more  useful  to  look  at  them 
in  the  latter,  i.e.  as  a  fall  in  the  purchasing  power  of 
the  product.  In  either  case  the  comparison  is  between 
the  cost  of  the  production  of  gold  and  the  purchasing 
power  of  gold.  If  this  purchasing  power  is  above  the 
cost  of  production  in  any  particular  mine,  it  will  pay 

1  Cf .  Mill,  Principles  of  Political  Economy,  Book  III,  Chapter 
IX,  §  2. 


Sec.  3]  INDIRECT  INFLUENCES    CONTINUED  103 

to  work  that  mine.  If  the  purchasing  power  of  gold 
is  lower  than  the  cost  of  production  of  any  particular 
mine,  it  will  not  pay  to  work  that  mine.  Thus  the 
production  of  gold  increases  or  decreases  with  an  in- 
crease or  decrease  in  the  purchasing  power  of  gold. 

So  much  for  the  inflow  of  gold  and  the  conditions 
regulating  it.  We  turn  next  to  outflow  or  consumption 
of  gold.  This  has  two  forms,  viz.  consumption  in  the 
arts  and  consumption  for  monetary  purposes. 

First  we  consider  its  consumption  in  the  arts.  If 
objects  made  of  gold  are  cheap  —  that  is,  if  the  prices 
of  other  objects  are  relatively  high  —  then  the  relative 
cheapness  of  the  gold  objects  will  lead  to  an  increase  in 
their  use  and  consumption.  Expressing  the  matter  in 
terms  of  money  prices,  when  prices  of  everything  else 
are  higher  and  people's  incomes  are  likewise  higher, 
while  gold  watches  and  gold  ornaments  generally  re- 
main at  their  old  prices,  people  will  use  and  consume 
more  gold  watches  and  ornaments. 

These  are  instances  of  the  consumption  of  gold  in  the 
form  of  commodities.  The  consumption  and  loss  of  gold 
as  coin  is  a  matter  of  abrasion,  of  loss  by  shipwreck 
and  other  accidents.  It  changes  with  the  changes  in 
the  amount  of  gold  in  use  and  in  its  rapidity  of  ex- 
change. The  outlets  from  this  reservoir  represent  the 
consumption  of  gold  coins  by  loss.  Just  as  production 
is  regulated  by  marginal  cost  of  what  is  produced,  so  is 
consumption  regulated  by  marginal  utility  of  what  is 
consumed.  This  is  not  the  place  to  enter  into  a  dis- 
cussion of  the  essential  symmetry  between  these  two 
marginal  magnitudes,  a  symmetry  often  lost  sight  of 
because  cost  is  usually  measured  objectively  and  util- 
ity subjectively.  Both  are  measurable  in  either  way. 
The  subjective  method  is  the  more  fundamental,  but 


104  THE   PURCHASING   POWER  OF  MONEY    [Chap.  VI 

takes  us  farther  away  from  our  present  discussion  than 
is  necessary  or  profitable. 

We  see  then  that  the  consumption  of  gold  is  stimu- 
lated by  a  fall  in  the  value  (purchasing  power)  of  gold, 
while  the  production  of  gold  is  decreased.  The  pur- 
chasing power  of  money,  being  thus  played  upon  by 
the  opposing  forces  of  production  and  consumption, 
is  driven  up  or  down  as  the  case  may  be.^ 


In  any  complete  picture  of  the  forces  determining 
the  purchasing  power  of  money  we  need  to  keep  prom- 
inently in  view  three  groups  of  factors :  (1)  the 
production  or  the  ''inflow"  of  gold  (i.e.  from  the  mines) ; 
(2)  the  consumption  or  "outflow"  (into  the  arts  and 
by  destruction  and  loss);  and  (3)  the  "stock"  or 
reservoir  of  gold  (whether  coin  or  bullion)  which 
receives  the  inflow  and  suffers  the  outflow.  The  re- 
lations among  these  three  sets  of  magnitudes  can  be 
set  forth  by  means  of  a  mechanical  illustration,  given 
in  Figure  5.  This  represents  two  connected  reservoirs 
of  Uquid,  Gb  and  G,n-  The  contents  of  the  first  reservoir 
represent  the  stock  of  gold  bullion,  and  the  contents 
of  the  second  the  stock  of  gold  money.     Since  purchas- 

1  The  theory  here  presented,  that  the  value  of  gold  bullion 
and  the  cost  of  production  of  gold  affect  prices  by  way  of  the 
quantity  of  money,  is  the  one  which  economists  have  generally 
held.  A  different  view  is  represented  by  Laughlin,  who  says,  "the 
quantity  of  money  used  as  the  actual  media  of  exchange  no  more 
determines  price  than  the  entries  of  deeds  and  conveyances  in 
the  county  records  determine  the  prices  of  the  land  whose  sale  is 
stated  in  the  papers  recorded,"  and  that  "price  is  an  exchange 
relation  between  goods  and  the  standard  money  commodity,  whether 
that  money  commodity  be  used  as  a  medium  of  exchange  or  not." 
See  The  Principles  of  Money,  New  York  (Scribner),  1903,  pp.  317 
and  318. 


Sec.  4] 


INDIRECT   INFLUENCES   CONTINUED 


105 


ing  power  increases  with  scarcity,  the  distance  from 
the  top  of  the  cisterns,  00,  to  the  surface  of  the  hquid, 
is  taken  to  represent  the  purchasing  power  of  gold  over 
other  goods.  A  lowering  of  the  level  of  the  liquid 
indicates  an  increase  in  the  purchasing  power  of  money, 
since  we  measure  this  purchasing  power  downward 
from  the  line  00  to  the  surface  of  the  liquid.  We  shall 
not  attempt  to  represent  other  forms  of  currency  ex- 
plicitly in  the  diagram.  We  have  seen  that  normally 
the  quantities  of  other  currency  are  proportional  to 


■tf      i-^"'-'  '-m  i  ^ 


Fig.  5. 


the  quantity  of  primary  money,  which  we  are  supposing 
to  be  gold.  Therefore,  the  variation  in  the  purchasing 
power  of  this  primary  money  may  be  taken  as  rep- 
resentative of  the  variation  of  all  the  currency.  We 
shall  now  explain  the  shapes  of  these  cisterns.  The 
shape  of  the  cistern  G,n  must  be  such  as  will  make  the 
distance  of  the  liquid  surface  below  00  decrease  with 
an  increase  of  the  liquid,  in  exactly  the  same  way  as 
the  purchasing  power  of  gold  decreases  with  an  increase 
in  its  quantity.  That  is,  as  the  quantity  of  liquid  in 
Gm  doubles,  the  distance  of  the  surface  from  the  line 


106  THE    PURCHASING   POWER   OF  MONEY    [Chap.  VI 

00  should  decrease  by  one  half.  In  a  similar  manner 
the  shape  of  the  gold  bullion  cistern  must  be  such  as 
will  make  the  distance  of  the  hquid  surface  below  00 
decrease  with  an  increase  of  the  liquid  in  the  same  way 
as  the  value  of  gold  bullion  decreases  with  an  increase 
of  the  stock  of  gold  bullion.  The  shapes  of  the  two 
cisterns  need  not,  and  ordinarily  will  not,  be  the  same, 
for  we  can  scarcely  suppose  that  halving  the  purchas- 
ing power  of  gold  will  always  exactly  double  the  amount 
of  bullion  in  existence. 

Both  reservoirs  have  inlets  and  outlets.  Let  us 
consider  these  in  connection  v/ith  the  bulUon  reservoir 
{Gi).  Here  each  inlet  represents  a  particular  mine 
supplying  bullion,  and  each  outlet  represents  a  partic- 
ular use  in  the  arts  consuming  gold  bullion.  Each 
mine  and  each  use  has  its  own  distance  from  00. 
There  are,  therefore,  three  sets  of  distances  from  00 : 
the  inlet  distances,  the  outlet  distances,  and  the  liquid- 
surface  distance.  Each  inlet  distance  represents  the 
cost  of  production  for  each  mine,  measured  in  goods ; 
each  outlet  distance  represents  the  value  of  gold  in 
some  particular  use,  likewise  measured  in  goods.  The 
surface  distance,  as  we  have  already  explained,  repre- 
sents the  value  of  bullion,  likewise  measured  in  goods, 
—  in  other  words,  its  purchasing  power. 

It  is  evident  that  among  these  three  sets  of  levels 
there  will  be  discrepancies.  These  discrepancies  serve 
to  interpret  the  relative  state  of  things  as  between 
bullion  and  the  various  flows  —  in  and  out.  If  an 
inlet  at  a  given  moment  be  above  the  surface  level, 
i.e.  at  a  less  distance  from  00,  the  interpretation  is 
that  the  cost  of  production  is  less  than  the  purchasing 
power  of  the  bullion.  Hence  the  mine  owner  will  turn 
on  his  spigot  and  keep  it  on  until,  perchance,  the  sur- 


Sec.  4]  INDIRECT  INFLUENCES   CONTINUED  107 

face  level  rises  to  the  level  of  his  mine,  —  i.e.  until 
the  surface  distance  from  00  is  as  small  as  the  inlet 
distance,  —  i.e.  until  the  purchasing  power  of  bullion 
is  as  small  as  the  cost  of  production.  At  this  point 
there  is  no  longer  any  profit  in  mining.  So  much  for 
inlets ;  now  let  us  consider  the  outlets.  If  an  outlet 
at  a  given  moment  be  below  the  surface  level,  —  i.e. 
at  a  greater  distance  from  00,  —  the  interpretation  is 
that  the  value  of  gold  in  that  particular  use  is  greater 
than  the  purchasing  power  of  bullion.  Hence  gold 
bullion  will  flow  into  these  uses  where  its  worth  is 
greater  than  as  bullion.  That  is,  it  will  flow  out  of  all 
outlets  helow  the  surface  in  the  reservoir. 

It  is  evident,  therefore,  that  at  any  given  moment, 
only  the  inlets  above  the  surface  level,  and  only  the 
outlets  below  it,  will  be  called  into  operation.  As  the 
surface  rises,  therefore,  more  outlets  will  be  brought 
into  use,  but  fewer  inlets.  That  is  to  say,  the  less  the 
purchasing  power  of  gold  as  bullion,  the  more  it  will 
be  used  in  the  arts,  but  the  less  profitable  it  will  be  for 
the  mines  to  produce  it,  and  the  smaller  will  be  the 
output  of  the  mines.  As  the  surface  falls,  more  inlets 
will  come  into  use  and  fewer  outlets. 

We  turn  now  to  the  money  reservoir  (G™) .  The  fact 
that  gold  has  the  same  value  either  as  bullion  or  as 
coin,  because  of  the  interflow  between  them,  is  in- 
terpreted in  the  diagram  by  connecting  the  bullion 
and  coin  reservoirs,  in  consequence  of  which  both  will 
(like  water)  have  the  same  level.  The  surface  of  the 
liquid  in  both  reservoirs  will  be  the  same  distance  be- 
low the  line  00,  and  this  distance  represents  the  value 
of  gold  or  its  purchasing  power.  Should  the  inflow 
at  any  time  exceed  the  outflow,  the  result  will  neces- 
sarily be  an  increase  in  the  stock  of  gold  in  existence. 


108  THE    PURCHASING    POWER   OF  MONEY    [Chap.  VI 

This  will  tend  to  decrease  the  purchasing  power  or 
value  of  gold.  But  as  soon  as  the  surface  rises,  fewer 
inlets  and  more  outlets  will  operate.  That  is,  the 
excessive  inflow  or  production  on  the  one  hand  will 
decrease,  and  the  deficient  outflow  or  consumption  on 
the  other  hand  will  increase,  checking  the  inequality 
between  the  outflow  and  inflow.  If,  on  the  other  hand, 
the  outflow  should  temporarily  be  greater  than  the  in- 
flow, the  reservoir  will  tend  to  subside.  The  purchas- 
ing power  will  increase ;  thus  the  excessive  outflow 
will  be  checked,  and  the  deficient  inflow  stimulated,  — 
restoring  equilibrium.  The  exact  point  of  equilibrium 
may  seldom  or  never  be  realized,  but  as  in  the  case 
of  a  pendulum  swinging  back  and  forth  through  a  posi- 
tion of  equilibrium,  there  will  always  be  a  tendency  to 
seek  it. 

It  need  scarcely  be  said  that  our  mechanical  diagram 
is  intended  merely  to  give  a  picture  of  some  of  the  chief 
variables  involved  in  the  problem  under  discussion. 
It  does  not  of  itself  constitute  an  argument,  or  add 
any  new  element ;  nor  should  one  pretend  that  it  in- 
cludes explicitly  all  the  factors  which  need  to  be  con- 
sidered. But  it  does  enable  us  to  grasp  the  chief 
factors  involved  in  determining  the  purchasing  power 
of  money.  It  enables  us  to  observe  and  trace  the 
following  important  variations  and  their  effects :  — 

First,  if  there  be  an  increased  production  of  gold  — 
due,  let  us  suppose,  to  the  discovery  of  new  mines  or 
improved  methods  of  working  old  ones  —  this  may  be 
represented  by  an  increase  in  the  number  or  size  of  the 
inlets  into  the  Gb  reservoir.  The  result  will  evidently 
be  an  increase  of  ''inflow"  into  the  bullion  reservoir, 
and  from  that  into  the  currency  reservoir,  a  consequent 
gradual  filling  up  of  both,  and  therefore  a  decrease  in 


Sec.  4]  INDIRECT   INFLUENCES   CONTINUED  109 

the  purchasing  power  of  money.  This  process  will  be 
checked  finally  by  the  increase  in  consumption.  And 
when  production  and  consumption  become  equal,  an 
equilibrium  will  be  established.  An  exhaustion  of  gold 
mines  obviously  operates  in  exactly  the  reverse  manner. 

Secondly,  if  there  be  an  increase  in  the  consumption 
of  gold  —  as  through  some  change  of  fashion  —  it 
may  be  represented  by  an  increase  in  the  number  or 
size  of  the  outlets  of  Gt.  The  result  will  be  a  draining 
out  of  the  bullion  reservoir,  and  consequently  a  de- 
creased amount  in  the  currency  reservoir :  hence  an 
increase  in  the  purchasing  power  of  gold,  which  in- 
crease will  be  checked  finally  by  an  increase  in  the  out- 
put of  the  mines  as  well  as  by  a  decrease  in  consump- 
tion. When  the  increased  production  and  the  decreased 
consumption  become  equal,  equilibrium  will  again  be 
reached. 

If  the  connection  between  the  currency  reservoir 
and  the  bullion  reservoir  is  closed  by  a  valve,  that 
is,  if  the  mints  are  closed  so  that  gold  cannot  flow 
from  bullion  into  money  (although  it  can  flow  in  the 
reverse  direction),  then  the  purchasing  power  of  the 
gold  as  money  may  become  greater  than  its  value  as 
bullion.  Any  increase  in  the  production  of  gold  will 
then  tend  only  to  fill  the  bullion  reservoir  and  decrease 
the  distance  of  the  surface  from  the  line  00,  i.e.  lower 
the  value  of  gold  bullion.  The  surface  of  the  liquid 
in  the  money  reservoir  will  not  be  brought  nearer  00. 
It  may  even  by  gradual  loss  be  lowered  farther  away. 
In  other  words,  the  purchasing  power  of  money  will 
by  such  a  valve  be  made  entirely  independent  of  the 
value  of  the  bullion  out  of  which  it  was  first  made. 

An  illustration  of  this  principle  is  found  in  the  history 
of  the  silver  currency  in  India.     After  long  discussion  the 


110  THE    PURCHASING    POWER   OF   MONEY     [Chap.  VI 

mints  of  India  were  closed  to  silver  in  1893.  Previous 
to  that  time  the  value  of  coined  silver  had  followed 
closely  the  value  of  silver  bullion,  but  the  closure 
produced  an  immediate  divergence  between  the  two. 
The  rupee  has  remained  independent  of  silver  ever  since ; 
and  during  the  first  six  years  —  until  1899  —  it  was 
independent  of  gold  also.  Its  present  relation  to  the 
latter  metal  will  be  discussed  in  the  next  chapter. 

We  have  now  discussed  all  but  one  of  the  outside  in- 
fluences upon  the  equation  of  exchange.  That  one  is 
the  character  of  the  monetary  and  banking  system 
which  affects  the  quantity  of  money  and  deposits. 
This  we  reserve  for  special  discussion  in  the  following 
chapter.  Meanwhile,  it  is  also  noteworthy  that  al- 
most all  of  the  influences  affecting  either  the  quantity 
or  the  velocities  of  circulation  have  been  and  are  pre- 
dominantly in  the  direction  of  higher  prices.  Almost 
the  only  opposing  influence  is  the  increased  volume 
of  trade;  but  this  is  partly  neutralized  by  increased 
velocities  due  to  the  increased  trade  itself.  We  may 
here  point  out  that  some  of  those  influences  discussed 
in  this  and  the  preceding  chapter  operate  in  more  than 
one  way.  Consider,  for  instance,  technical  knowledge 
and  invention,  which  affect  the  equation  of  exchange 
by  increasing  trade.  So  far  as  these  increase  trade, 
the  tendency  is  to  decrease  prices ;  but  so  far  as  they 
develop  metallurgy  and  the  other  arts  which  increase 
the  production  and  easy  transportation  of  the  precious 
metals,  they  tend  to  increase  prices.  So  far  as  they 
make  the  transportation  and  transfer  of  money  and 
deposits  quicker,  they  also  tend  to  increase  prices. 
So  far  as  they  lead  to  the  development  of  the  art  of 
banking,  they  likewise  tend  to  increase  prices,  both  by 
increasing  deposit  currency  {M')  and  by  increasing  the 


Sec.  4]  INDIRECT  INFLUENCES   CONTINUED  1 1 1 

velocity  of  circulation  both  of  money  and  deposits. 
So  far  as  they  lead  to  the  concentration  of  population 
in  cities,  they  tend  to  increase  prices  by  accelerating 
circulation. 

Finally,  so  far  as  per  capita  trade  is  increased  through 
this  or  any  other  cause,  there  is  a  tendency  to  decrease 
prices.  What  the  net  effect  of  the  development  of  the 
arts  may  be  during  any  given  period  will  depend  on  the 
predominant  direction  in  which  the  arts  are  developed. 


CHAPTER  VII 

INFLUENCE    OF  MONETARY   SYSTEMS   ON   PURCHASING 

POWER 


Thus  far  we  have  considered  the  influences  that  de- 
termine the  purchasing  power  of  money  when  the  money 
in  circulation  is  all  of  one  kind.  The  illustration  given 
in  the  previous  chapter  shows  how  the  money  mecha- 
nism operates  when  a  single  metal  is  used.  We  have 
now  to  consider  the  monetary  systems  in  which  more 
than  one  kind  of  money  is  used. 

One  of  the  first  difficulties  in  the  early  history  of 
money  was  that  of  keeping  two  (or  more)  metals  in 
circulation.  One  of  the  two  would  become  cheaper  than 
the  other,  and  the  cheaper  would  drive  out  the  dearer. 
This  tendency  was  observed  by  Nicolas  Oresme, 
afterwards  Count  Bishop  of  Lisieux,  in  a  report  to 
Charles  V  of  France,  about  1366,  and  by  Copernicus 
about  1526  in  a  report  or  treatise  written  for  Sigis- 
mund  I,  King  of  Poland.^  Macleod  in  his  Elements 
of  Political  Economy,  published  in  1857,^  before  he  had 
become  aware  of  the  earlier  formulations  of  Oresme 
and  Copernicus,^  gave  the  name  ''Gresham's  Law"  to 
this  tendency,  in  honor  of  Sir  Thomas  Gresham,  who 
stated  the  principle  in  the  middle  of  the  sixteenth  cen- 

1  Henry  Dunning  Macleod,  The  History  of  Economics,  New  York 
(Putnam),  1896,  pp.  37  and  38. 

2  P.  477. 

» Macleod,  The  History  of  Economics,  pp.  38  and  39. 

112 


Sec.  IJ  INFLUENCE    OF  MONETARY   SYSTEMS  113 

tury.  The  tendency  seems  in  fact,  to  have  been  rec- 
ognized even  among  the  ancient  Greeks,  being  men- 
tioned in  the  "Frogs"  of  Aristophanes  :  *  — 

^'For  your  old  and  standard  pieces  valued  and  approved  and  tried, 
Here  among  the  Grecian  nations  and  in  all  the  world  beside, 
Recognized  in  every  realm  for  trusty  stamp  and  pure  assay. 
Are  rejected  and  abandoned  for  the  trash  of  yesterday, 
For  a  vile,  adulterate  issue,  drossy,  counterfeit,  and  base 
Which  the  traffic  of  the  City  passes  current  in  their  place." 

Gresham's  or  Oresme's  Law  is  ordinarily  stated  in 
the  form,  ''Bad  money  drives  out  good  money,"  for 
it  was  usually  observed  that  the  badly  worn,  defaced, 
light-weight,  ''clipped,"  "sweated,"  and  otherwise  de- 
teriorated money  tended  to  drive  out  the  full-weight, 
freshly  minted  coins.  This  formulation,  however,  is 
not  accurate.  It  is  not  true  that  "bad"  coins,  e.g. 
worn,  bent,  defaced,  or  even  clipped  coins,  will  drive 
out  other  money  just  because  of  their  worn,  bent,  de- 
faced, or  clipped  condition.  Accurately  stated,  the 
Law  is  simply  this :  Cheap  money  will  drive  out  dear 
money.  The  reason  the  cheaper  of  two  moneys  always 
prevails  is  that  the  choice  of  the  use  of  money  rests 
chiefly  with  the  man  who  gives  it  in  exchange,  not 
with  the  man  who  receives  it.  When  any  one  has 
the  choice  of  paying  his  debts  in  either  of  two  moneys, 
motives  of  economy  will  prompt  him  to  use  the 
cheaper.  If  the  initiative  and  choice  lay  principally 
with  the  person  who  receives,  instead  of  the  person  who 
pays  the  money,  the  opposite  would  hold  true.  The 
dearer  or  "good"  money  would  then  drive  out  the 
cheaper  or  "bad"  money. 

What  then  becomes  of  the  dearer  money  ?    It  may 

1 893-898,  Frere's  translation. 


114  THE    PURCHASING    POWER   OF   MONEY        [Chap.  Vli 

be  hoarded,  or  go  into  the  melting  pot,  or  go  abroad,  — 
hoarded  and  melted  from  motives  of  economy,  and 
sent  abroad  because,  where  foreign  trade  is  involved,  it 
is  the  foreigner  who  receives  the  money,  rather  than 
ourselves  who  give  it,  who  dictates  what  kind  of  money 
shall  be  accepted.  He  will  take  only  the  best,  because 
our  legal-tender  laws  do  not  bind  him. 

The  better  money  might  conceivably  be  used  in  ex- 
change at  a  premium,  i.e.  at  its  bullion  value;  but  the 
difficulties  of  arranging  payments  in  it,  which  would 
be  satisfactory  to  both  parties,  are  such  that  in  practice 
it  is  never  so  used  in  large  quantities.  In  fact,  the  force 
of  Gresham's  Law  is  so  great  that  it  will  even  sacrifice 
the  convenience  of  a  whole  nation.  For  instance,  in 
Italy  fifteen  years  ago  the  overissue  of  paper  money 
drove  not  only  gold  across  the  Alps,  but  also  silver 
and  copper.  These  could  circulate  in  Southern  France 
at  a  par  with  corresponding  coins  there  because  France 
and  Italy  belonged  to  the  Latin  Union.  Consequently, 
for  a  time  there  was  very  little  small  change  left,  below 
the  denomination  of  5  lire  notes.  Customers  at  retail 
stores  often  found  it  impossible  to  make  their  pur- 
chases because  they  lacked  the  small  denominations 
necessary,  and  because  the  storekeeper  lacked  the  same 
small  denominations,  and  could  not  make  change.  To 
meet  the  difficulty,  30,000,000  of  1  lire  notes  were 
issued,  and  these  were  so  much  in  demand  that  dealers 
paid  a  premium  for  them. 

Gresham's  Law  applies  not  only  to  two  rival  moneys 
of  the  same  metal;  it  applies  to  all  moneys  that  cir- 
culate concurrently.  Until  ''milling"  the  edges  of 
coins  was  invented  and  a  ''limit  of  tolerance"  of  the 
mint  (deviation  from  the  standard  weight)  was  adopted, 
much  embarrassment  was  felt  in  commerce  from  the 


Sec.  2]  INFLUENCE    OF  MONETARY  SYSTEMS  115 

fact  that  the  chpping  and  debasing  of  coin  was  a  com- 
mon practice.  Nowadays,  however,  any  coin  which  has 
been  so  "sweated"  or  cUpped  as  to  reduce  its  weight 
appreciably  ceases  to  be  legal  tender,  and  being  com- 
monly rejected  by  those  to  whom  it  is  offered  ceases 
to  be  money.  Within  the  customary  ^  or  legal  limits  of 
tolerance,  however  —  that  is,  as  long  as  the  cheaper 
money  retains  the  "money"  power  —  it  will  drive 
out  the  dearer. 

§2 

The  obvious  effect  of  Gresham's  Law  is  to  decrease  \ 
the  purchasing  power  of  money  at  every  opportunity,  j 
The  history  of  the  world's  currencies  is  largely  a  record 
of  money  debasements,  often  at  the  behest  of  the 
sovereign.  Our  chief  purpose  now,  in  considering 
Gresham's  Law,  is  to  formulate  more  fully  the  causes 
determining  the  purchasing  power  of  money  under 
monetary  systems  subject  to  the  operation  of  Gresham's 
Law.     The  first  application  is  to  bimetallism. 

In  order  to  understand  fully  the  influence  of  any 
monetary  system  on  the  purchasing  power  of  money, 
we  must  first  understand  how  the  system  works. ^  It 
has  been  denied  that  bimetallism  ever  did  work  or  can 
be  made  to  work,  because  the  cheaper  metal  will  drive 
out  the  dearer.  Our  first  task  is  to  show,  quite  irrespec- 
tive of  its  desirability,  that  bimetallism  can  and  does 
"work"  under  certain  circumstances,  but  not  under 
others.  To  make  clear  when  it  will  work  and  when  it 
will  not  work,  we  shall  continue  to  employ  the  mechani- 

'  Sometimes  custom  is  less  strict  than  law.  For  instance,  in 
California  worn  gold  coin  below  the  mint  limit  of  tolerance  con- 
tinues to  circulate.     It  is  called  "bank  gold." 

'Irving  Fisher,  "The  Mechanics  of  Bimetallism,"  (British) 
Economic  Journal,  September,  1894,  pp.  527-536. 


116         THE    PURCHASING    POWER   OF  MONEY        [Chap.  VH 

cal  illustration  ^  of  the  last  chapter,  in  which  the  amount 
of  gold  bullion  is  represented  by  the  contents  of  res- 
ervoir Gb  (Figs.  6,  7).  Here,  as  before,  we  represent 
the  purchasing  power  or  value  of  gold  by  the  distance 
of  the  water  level  below  the  zero  level,  00.  In  the 
last  chapter,  our  figure  represented  only  one  metal, 
gold,  and  represented  that  metal  in  two  reservoirs,  —  the 
bullion  reservoir  and  the  coin  reservoir.  We  shall  now, 
one  step  at  a  time,  elaborate  that  figure.  First,  as  in 
Figure  6  a,  we  add  a  reservoir  for  silver  bullion  {St),  a 


reservoir  of  somewhat  different  shape  and  size  from 
Gi.     This  reservoir  may  be  used  i  to  show  the  relation 

^  In  its  present  application  it  is  somewhat  like  a  symbolism 
suggested  by  Jevons  in  his  Money  and  the  Mechanism  of  Exchange, 
New  York  (Appleton),  1896,  p.  140. 


Sec.  2]  INFLUENCE   OF  MONETARY  SYSTEMS  117 

between  the  value  or  purchasing  power  of  silver  and 
its  quantity  in  the  arts  and  as  bullion.  Here,  then, 
are  three  reservoirs.  At  first  the  silver  one  is  entirely 
isolated;  but  after  a  while  we  shall  connect  it  with 
the  middle  one.  For  the  present,  let  us  suppose  that 
the  middle  one,  which  contains  money,  is  entirely  filled 
with  gold  money  only  (Fig.  6  a),  no  silver  being  yet 
used  as  money.  In  other  words,  the  monetary  system 
is  the  same  as  that  discussed  in  the  last  chapter.  The 
only  change  we  have  introduced  is  to  add  to  the  pic- 
ture another  reservoir  {St),  entirely  detached,  showing 
the  quantity  and  value  of  silver  bullion. 

We  next  suppose  a  pipe  opened  at  the  right,  connect- 
ing Sb  with  the  money  reservoir;  that  is,  we  introduce 
bimetallism.  Under  bimetallism,  governments  open 
their  mints  to  the  free  coinage  of  both  metals  at  a  fixed 
ratio,  i.e.  a  fixed  ratio  between  the  said  metals.  For 
instance,  if  a  silver  dollar  contains  16  grains  of  silver 
for  every  grain  of  gold  in  a  gold  dollar,  the  ratio  is  said 
to  be  16  to  1.  Under  this  system,  the  debtor  has  the 
option,  unless  otherwise  bound  by  his  contract,  of  mak- 
ing payment  either  in  gold  or  in  silver  money.  These, 
in  fact,  are  the  two  requisites  of  complete  bimetallism, 
viz.  (1)  the  free  and  unlimited  coinage  of  both  metals  at 
a  fixed  ratio,  and  (2)  the  unlimited  legal  tender  of  each 
metal  at  that  ratio. ^  These  new  conditions  are  repre- 
sented in  Figure  6  b  (and  later,  Fig.  7  b) ,  where  a  pipe  gives 
silver  an  entrance  into  the  money  or  central  reservoir.^ 

1  The  possibility  of  government's  fixing  any  ratio  between  gold 
and  silver  to  which  the  market  ratio  will  conform  has  been  so  bitterly 
disputed  that  in  addition  to  the  positive  argument  contained  in  the 
text,  a  negative  criticism  of  what  are  believed  to  be  the  chief  fal- 
lacies underlying  these  disputes  is  inserted  in  §  1  of  the  Appendix 
to  (this)  Chapter  VII. 

2  Of  course  a  unit  of  water  represents  gold  and  silver  at  their 


118         THE    PURCHASING   POWER   OF  MONEY        [Chap.  Vlt 

What  we  are  about  to  represent  is  not  the  relations 
between  mines,  bullion,  and  arts,  but  the  relations  be- 
tween bulhon  (two  kinds)  and  coins.  We  may,  there- 
fore, disregard  for  the  present  all  inlets  and  outlets 
except  the  connections  between  the  bulhon  reservoirs 
and  coin  reservoir. 

Now  in  these  reservoirs  the  surface  distances  below 
00  represent,  as  we  have  said,  purchasing  power 
of  gold  and  silver.  But  each  unit  of  silver  (say  each 
drop  of  silver  water,  whether  as  money  or  as  bulhon) 
contains  sixteen  times  as  many  grains  as  each  unit  of 
gold  (say  each  drop  of  gold  water,  whether  as  money 
or  as  bullion).  That  is,  a  unit  of  water  represents  a 
dollar  of  gold  or  a  dollar  of  silver.  All  we  wish  to 
represent  is  the  relative  purchasing  power  of  corre- 
sponding units. 

The  waters  representing  gold  and  silver  money  are 
separated  by  a  movable  film  /.  In  Figure  6  a  this  film 
is  at  the  extreme  right ;  in  Figure  6  6,  at  the  extreme 
left;  in  Figure  7  a,  again  at  the  right;  and  in  Figure  7  h, 
midway.  The  a  figures  represent  conditions  before 
the  mints  are  opened  to  silver.  The  h  figures  repre- 
sent conditions  after  they  have  been  opened  and  Gres- 
ham's  Law  has  operated.  If,  just  previous  to  the  in- 
troduction of  bimetallism,  the  silver  level  in  S^  is  below 
the  gold  level  in  Gj,  the  statute  introducing  bimetallism 
will  be  inoperative,  i.e.  the  silver  bullion  will  not  flow 
uphill,  as  it  were,  into  the  money  reservoir ;  but  if,  as 
in  Figure  6  a  or  in  7  a,  the  silver  level  is  higher,  then  as 

coining  weights.  If  the  bimetallic  ratio  is  16  to  1,  the  cisterns 
must  be  so  constructed  that  a  cubic  inch  of  water  shall  represent 
an  ounce  of  gold  or  16  ounces  of  silver  and  that  the  number  of 
inches  separating  the  surfaces  of  liquid  from  00  shall  represent  the 
marginal  utility  of  an  ounce  of  gold  and  of  16  ounces  of  silver, 
respectively. 


Sec.  2] 


INFLUENCE    OF   MONETARY   SYSTEMS 


119 


soon  as  the  mints  are  open  to  silver,  it  will  flow  into 
circulation.  Being  at  first  cheaper  than  gold,  it  will 
push  out  the  gold  money  through  the  left  tube  (i.e.  by- 
melting)  into  the  bullion  market.  This  expulsion  of 
gold  may  be  complete,  as  shown  in  Figure  6  b,  or  only 
partial,  as  shown   in  Figure  7  b.    The  expulsion  will 


FiQ.  7. 

continue  just  as  long  as  there  is  a  premium  on  gold ; 
that  is,  as  long  as  the  silver  level  in  the  bullion  reservoir 
is  above  the  gold  level  in  the  money  reservoir ;  i.e.  as 
long  as  silver  bullion  is  cheaper  than  gold  money. 

Let  mm,  as  shown  in  Figure  6  a,  be  the  mean  level ; 
that  is,  a  level  such  that  the  volume  x  above  it  equals 
the  combined  vacant  volumes  y  and  z  below  it.  This 
line,  mm,  remains  the  mean  level,  whatever  may  be  the 


120        THE    PURCHASING   POWER   OF  MONEY        [Chap.  VII 

distribution  of  the  contents  among  the  three  reservoirs. 
As  soon  as  the  connecting  pipe  is  inserted,  silver  will 
flow  into  the  money  reservoir  and,  in  accordance  with 
Gresham's  Law,  will  displace  gold. 

Here  we  have  to  distinguish  two  cases  :  (1)  when  the 
silver  x  above  the  mean  hne,  mm,  exceeds  the  total  con- 
tents of  the  money  reservoir  below  this  line;  (2)  when  x 
is  less  than  said  lower  contents.  In  the  first  case,  it 
is  evident  that  silver  will  sweep  gold  wholly  out  of 
circulation,  as  shown  in  Figure  6  b,  where  the  film  has 
moved  from  the  extreme  right  to  the  extreme  left. 
The  contents  of  silver  in  the  bullion  reservoir  are  less 
than  before,  and  the  contents  of  gold  in  the  bullion 
reservoir  greater  than  before. 

But  this  redistribution  is  only  the  first  effect  of  open- 
ing the  mints  to  silver.  The  balance  between  produc- 
tion and  consumption  has  been  upset  both  for  gold 
and  for  silver.  The  increased  value  of  silver  (lowered 
level  in  Sh)  has  stimulated  production,  bringing  into 
operation  silver  mines  (uncovered  inlets  at  right) ; 
and,  on  the  other  hand,  the  decreased  value  of  gold 
(raised  level  in  Gh)  has  discouraged  gold  production, 
shutting  off  gold  mines  (covered  inlets  at  left).  Like 
alterations  are  effected  in  the  outflows,  i.e.  the  con- 
sumption, waste,  and  absorption  of  each  metal. 

The  result  is  that  the  levels  resulting  from  the 
first  redistribution  will  not  necessarily  be  permanent. 
They  may  recede  toward  their  original  respective 
levels,  and  under  all  ordinary  conditions  will  do  so. 
But  in  any  case,  —  and  this  is  the  point  to  be  em- 
phasized, —  they  cannot  return  entirely  to  those  levels. 
Such  a  supposition  would  be  untenable,  as  the  follow- 
ing reasoning  shows.  Suppose,  for  the  moment,  that 
silver  should  return  to  its   original  level.     Then  the 


Sec.  3]  INFLUENCE    OF  MONETARY  SYSTEMS  121 

silver  inflow  (production)  would  also  return  to  its  origi- 
nal rate  dependent  on  that  level,  but  the  silver  outflow 
(consumption,  waste,  etc.)  would  be  greater  than 
originally.  The  consumption  in  the  arts  would  be  the 
same;  but  the  waste  and  absorption  of  silver  money 
constitute  an  additional  drain.  Therefore,  consump- 
tion (equal  to  production  before)  will  now  exceed  pro- 
duction, and  the  high  original  level  cannot  be  main- 
tained. The  conclusion  follows  that,  whatever  the  new 
level  of  permanent  equilibrium,  it  lies  below  the  old. 
The  same  argument,  mutatis  mutandis,  proves  that  for 
gold  the  new  level  of  permanent  equilibrium  lies  above 
the  old.  The  gap  between  the  two  original  levels  has 
therefore  been  reduced.  Even  though  bimetallism  has 
failed  to  bring  about  a  concurrent  circulation  of  both 
metals  and  a  parity  of  values  at  the  given  coinage 
ratio,  it  has  resulted  in  reducing  the  value  of  the  dearer 
metal  (gold)  and  increasing  that  of  the  cheaper  (silver). 
This  effect  of  mutual  approach  will  be  referred  to  in 
discussing  the  second  case  which  follows. 

§3 

So  much  for  the  first  case,  where  x  is  larger  than  the 
contents  of  the  money  reservoir  below  mm.  In  the 
second  case,  x  is  supposed  to  be  smaller  than  the  con- 
tents of  the  money  reservoir  below  the  line  mm ;  that 
is,  there  is  not  enough  silver  to  push  all  the  gold  out 
of  circulation.  Under  these  circumstances,  disregard- 
ing for  the  moment  any  change  in  production  or 
consumption,  the  opening  of  the  pipe  —  the  opening 
of  the  mints  to  silver  —  will  bring  the  whole  system 
of  liquids  to  the  common  level  mm.  In  other  words, 
the  premium  on  gold  bullion  will  disappear  (Fig.  7  6), 
and  its  purchasing  power  and  the  purchasing  power 


122        THE    PURCHASING   POWER   OF  MONEY        [Chap.  VII 

of  silver  bullion  will  be  a  mean  between  their  original 

purchasing  powers,  this  mean  being  the  distance  of  the 

I       mean  line,  mm,  below  00.     In  other  words,  bimetallism 

1       in  this  case   succeeds;   that   is,  it  will    establish    and 

V.    maintain  an  equality  for  a  time  between  the  gold  and 

silver  dollars  in  the  money  reservoir. 

But  the  equilibrium  which  we  have  just  found  is  a 
mere  equalization  of  levels  produced  by  a  redistribution 
of  the  existing  stocks  of  gold  and  silver  among  the 
various  reservoirs.  It  will  be  disturbed  as  soon  as 
these  stocks  are  disturbed.  A  permanent  equilibrium 
requires  that  the  stocks  shall  remain  the  same,  —  re- 
quires, in  other  words,  an  equality  between  production 
and  consumption  for  each  metal.  After  the  inrush  of 
silver  from  the  silver  bullion  to  the  money  reser- 
voir, it  is  evident  that  the  production  and  consump- 
tion of  gold  need  no  longer  be  equal  to  each  other, 
nor  need  the  production  and  consumption  of  silver 
be  equal  to  each  other.  The  same  stimulation  of  sil- 
ver production  and  discouragement  of  gold  production 
will  occur  that  occurred  in  the  case  considered  in  the 
last  section.  The  result  may  be  that  silver  will,  in 
the  end,  entirely  displace  gold;  or  again  it  may  fail  to 
do  so. 

There  may  be,  then,  two  possibilities.  One  possibility 
is  obvious,  namely,  that  gold  may  be  completely  driven 
out,  the  result  being  the  same  as  already  represented  in 
the  lower  part  of  Figure  6.  In  the  second  possibility, 
gold  will  not  be  pushed  out. 

The  reality  of  this  second  possibility  will  be  clear  if 
we  attempt  first  to  deny  it.  Suppose,  therefore,  that  the 
film  /  be  at  the  extreme  left,  and  permanent  equilib- 
rium finally  established.  In  the  illustrative  mechanism 
the  gold  level  will  be  lower  than  before,  and  the  silver 


Sec.  3]  INFLUENCE   OF  MONETARY   SYSTEMS  123 

level  higher.  How  much  lower  and  higher  depends 
evidently  on  technical  conditions  of  the  production  and 
consumption  corresponding  to  the  situation.  It  is  of 
course  not  inconceivable  that  the  gold  level  may  be  so 
much  lower  and  the  silver  level  so  much  higher  as  to 
make  their  relative  positions  reversed,  i.e.  to  make 
the  gold  level  higher  than  the  silver  level.  But  in  this 
event  it  is  quite  impossible  that  the  film  /  should  be 
at  the  left.  Gold,  now  being  the  cheaper,  would  flow 
into  circulation  and  displace  silver.  Under  the  con- 
ditions we  are  now  imagining,  the  film  cannot  stay 
at  either  extreme.  If  it  is  at  the  right,  silver  will  be 
cheaper  than  gold  and  will  move  it  leftward ;  if  it 
is  at  the  left,  gold  will  be  cheaper  than  silver  and 
will  move  it  rightward.  Under  these  circumstances, 
evidently,  equilibrium  must  lie  between  these  extremes, 
as  in  Figure  7  b.  The  conditions  of  production  and  con- 
sumption under  which  bimetallism  can  succeed  are 
therefore  (1)  that  under  silver  monometallism  a  gold 
dollar  would  in  equilibrium  be  cheaper  than  a  silver 
dollar,  and  (2)  that  under  gold  monometallism  silver 
would  be  cheaper  than  gold.  A  bimetallic  level,  there- 
fore, when  bimetallism  is  feasible,  must  always  lie 
between  the  levels  which  the  two  metals  would  have 
assumed  under  gold  monometallism,  gold  being  currency 
and  silver  not,  and  for  the  same  reasons  it  must  lie 
between  the  levels  which  the  two  metals  would  have 
under  silver  monometallism,  silver  being  currency  and 
gold  not.^  In  all  our  reasoning  we  have  supposed  a 
given  legal  ratio  between  the  two  metals.  But  bimetal- 
lism, impossible   at   one  ratio,   is   always   possible   at 

^  But  it  does  not  necessarily  lie  between  the  level  of  the  currency 
under  gold  monometallism  and  its  level  under  silver  mono- 
metallism. 


124         THE    PURCHASING    POWER    OF   MONEY         [Chap.  VII 

another.  There  will  always  be  two  limiting  ratios  be- 
tween which  bimetalUsm  is  possible.^ 

It  is  easy  to  show  that  the  two  limiting  ratios  for  a 
single  nation  are  narrower  than  for  a  combination  of 
nations,  since  the  currency  reservoir  is,  for  one  nation, 
smaller  than  for  many,  while  the  arts  reservoirs  are 
virtually  larger  by  the  amount  of  the  monometalHc 
currencies  of  the  remaining  nations.  When  bimetalUsm 
has  broken  down  at  one  ratio,  it  can  always  be  set  in 
operation  again  at  another,  but  the  transition  requires 
a  depreciation  of  the  currency.  The  only  way  of  re- 
introducing the  metal  which  has  passed  out  of  the 
currency  reservoir  is  by  lowering  the  amount  of  it  in 
the  monetary  unit,  —  unless  the  still  more  drastic 
measure  is  adopted  of  raising  the  coinage  weight  of 
money  alread}'  in  circulation. 

I  It  should  also  be  pointed  out  that  two  nations  can- 
not both  maintain  bimetallism  at  two  different  ratios 
unless  the  difference  is  less  than  the  cost  of  shipment. 
One  of  the  two  nations  would  lose  the  metal  which  it 
undervalued  and  find  itself  on  a  monometallic  basis. 

A  few  additional  observations  may  now  be  stated. 
The  temporary  and  normal  equiUbriums  which  have 
been  considered  separately  are  in  fact  quite  distinctly 
separated  in  time.!  The  time  of  redistributing  existing 
stocks  of  metal,  according  to  a  newly  enacted  law, 
depends  on  the  rapidity  of  transportation,  melting,  and 
minting,  and  would  be  measured  in  months  or  weeks. 
Normal  equihbrium,  however,  depends  on  the  slow 
working  of  changes  in  the  rates  of  production  and 
consumption,  and  would  be  measured  in  years.  The 
normal  equilibrium,  if  once  established,  is  permanent  so 
long  as  the  conditions  of  production  and  consumption 
1  See  §  2  of  Appendix  to  (this)  Chapter  VII. 


Sec.  3]  INFLUENCE    OF   MONETARY   SYSTEMS  125 

do  not  change.  Slight  alterations  of  these  conditions  — 
the  exhaustion  of  mines,  the  discovery  of  new  leads, 
etc.  —  will  cause  slight  variations  in  the  proportions  of 
gold  and  silver  money,  that  is,  in  the  position  of  the 
film  /.  The  oscillations  of  this  film  (and  not  of  the 
price  ratio  as  in  the  case  of  two  unconnected  com- 
modities) reflect  these  changing  conditions.  But,  in 
all  probability,  this  film  will  sooner  or  later  reach  one 
of  its  limits.  The  probable  time  for  such  an  event  is, 
however,  very  long.  The  gold  currency  of  the  world 
is,  roughly  speaking,  perhaps  $5,000,000,000 ;  the  annual 
production  of  silver,  reckoning  at  its  present  market 
price,  is  roughly  about  $100,000,000.  Supposing  a 
system  of  international  bimetallism  at,  say,  36  to  1  to 
be  initially  in  normal  equilibrium,  consider  the  effect 
of  an  enormous  increase  in  the  silver  production,  say 
a  half,  or  $50,000,000.  Then  a  hundred  years  would 
be  required  to  push  out  gold  without  taking  into  account 
the  fact  that,  as  the  pushing  proceeds,  the  excess  of 
production  over  consumption  steadily  declines.  If 
this  excess  dwindles  uniformly  from  $50,000,000  to  zero, 
the  period  would  be  double,  or  two  hundred  years. 
When  we  add  to  these  considerations  the  fact  that, 
while  the  stimulus  to  the  production  of  one  metal  acts 
quickly,  the  ensuing  check  to  the  production  of  the 
other  acts  more  slowly,  owing  to  the  fixity  of  the  ''sunk" 
capital,  and  that,  therefore,  the  volume  of  the  currency 
is  greater  at  the  end  than  at  the  beginning;  also  the 
fact  that  the  currency  reservoir  is  itself  constantly 
expanding ;  and  finally  the  fact  that  fluctuations  of 
production  are  likely  to  be  in  either  direction,  and  for 
either  metal,  we  may  be  tolerably  confident  that,  if 
initially  successful  with  the  film  near  the  middle  position, 
international    bimetallism    would    continue    successful 


126         THE    PURCHASING    POWER   OF   MONEY         [Chap.  VII 

for  many  generations.  The  initial  success  depends, 
as  has  been  seen,  upon  the  ratio  enacted. 

It  is  to  be  observed  that  bimetalUsm  can  never  avoid 
a  slight  premium.  On  the  contrary,  it  is  this  difference 
of  level  which  supplies  the  force  which  compells  change 
from  one  point  of  equiUbrium  to  another.^ 

In  a  series  of  years,  the  bimetallic  level  remains 
intermediate  between  the  changing  levels  which  the 
two  metals  would  separately  follow.  Bimetallism 
spreads  the  effect  of  any  single  fluctuation  over  the 
combined  gold  and  silver  markets. ^  The  steadying 
power  of  bimetallism  depends  on  the  breadths  of  the  res- 
ervoirs, and  not  on  the  position  of  the  film  /.  It  remains 
in  full  force,  no  matter  what  may  be  the  proportions 

^  As  long  as  the  premium  lasts,  the  cheaper  metal  will  doubtless 
circulate  somewhat  faster,  and  the  dearer  somewhat  more  slowly, 
than  when  there  is  no  premium.  This  may,  if  desired,  be  repre- 
sented by  conceiving  the  thickness  of  the  currency  reservoir  to 
decrease  on  the  one  side  of  /  and  increase  on  the  other,  making  one 
metal  "go  farther"  (cover  more  area  in  the  diagram)  than  normally, 
and  hasten  the  motion  of  /  to  the  equilibrium  point.  Sluggishness 
(increase  of  thickness),  of  which  "hoarding"  is  the  chief  application, 
is  referred  to  below. 

"■  To  represent  the  steadying  effect  on  a  single  fluctuation,  we 
observe  that  under  bimetallism  the  three  reservoirs  act  as  one. 
Therefore,  compared  with  monometallism,  the  fluctuations  are 
diminished  in  the  inverse  ratio  of  the  liquid  surfaces  over  which 
the  fluctuations  spread.  Thus,  if  the  combined  breadths  of  the 
two  left  reservoirs  at  water  level  are  two  thirds  of  the  combined 
breadths  of  the  three,  an  influx  of  gold  which,  if  distributed  only 
over  the  two  reservoirs,  would  make  a  layer  an  inch  in  depth, 
would,  over  the  three,  have  a  depth  of  two  thirds  of  an  inch.  Like- 
wise the  right  reservoir  being  one  third  the  aggregate  width,  an 
inch  fluctuation  of  silver,  when  merely  merchandise,  would  be 
reduced  to  one  third  of  an  inch,  when  connection  is  maintained 
with  the  money  reservoir.  The  breadths  of  the  reservoir,  which 
here  play  the  important  role,  are  the  rate  of  increase  of  commodity 
relative  to  decrease  of  marginal  utility.  The  law  of  inverse  breadth 
applies  with  exactness  only  to  static,  or  short-time  readjustments. 


Sec.  4]  INFLUENCE    OF  MONETARY  SYSTEMS  127 

of  gold  and  silver  money,  and  is  as  great  when  only 
one  nation  is  bimetallic  as  when  the  whole  world  adopts 
the  system.  Even  if  only  Switzerland  had  a  system 
of  bimetallism  in  successful  operation,  it  would,  until 
its  breakdown,  keep  together  and  equalize  the  currencies 
of  the  whole  world,  wherever  either  gold  or  silver  was 
standard.  In  fact,  the  world  would  have  all  the  benefits 
of  bimetallism  enjoyed  by  Switzerland  without  its  evils 
and  dangers.  This  international  function  would  cease 
abruptly  as  soon  as  the  system  of  bimetallism  should 
fail. 

It  should  be  pointed  out  that  the  equalizing  effect 
maintained  is  relative  only.  It  is  conceivable  that  one 
metal  would  be  steadier  alone  than  when  joined  to  the 
other.  In  a  later  chapter  we  shall  consider  the  extent 
to  which  this  equalization  is  an  advantage.  Here 
we  confine  ourselves  to  showing  merely  the  mechanical 
operation  of  the  bimetallic  system.^ 

§4 

Bimetallism  is  to-day  a  subject  of  historical  interest 
only.  It  is  no  longer  practiced;  but  its  former  prev- 
alence has  left  behind  it  in  many  countries,  including 
France  and  the  United  States,  a  monetary  system 
which  is  sometimes  called  the  ^^ limping ' '  ptan d ard . 
Such  a  system  comes  about  when,  in  a  system  of 
bimetallism,  before  either  metal  can  wholly  expel  the 
other,  the  mint  is  closed  to  the  cheaper  of  them,  but  the 
coinage  that  has  been  accomplished  up  to  date  is  not 
recalled.  Suppose  silver  to  be  the  metal  thus  excluded, 
as  in  France  and  the  United  States.     Any    money 

^Cf.  Leonard  Darwin,  Bimetallism,  London  (Murray),  1897,  341 
pp. ;  Bertrand  Nogaro,  "U experience  bimetalliste,"  Revue  d' economic 
politique,  1908. 


128         THE    PURCHASING    POWER   OF   MONEY        [Chap.  VII 

already  coined  in  that  metal  and  in  circulation  is  kept 
in  circulation  at  par  with  gold.  This  parity  may  con- 
tinue even  if  limited  additional  amounts  of  silver  be 
coined  from  time  to  time.  There  will  then  result  a 
difference  in  value  between  silver  bullion  and  silver  coin, 
the  silver  coin  being  overvalued.  This  situation  is 
represented  in  Figure  8.  Here  the  pipe  connection 
between   the  money  reservoir   and   the   silver-bullion 


Fig.  8. 


reservoir  has  been,  as  it  were,  cut  off,  or,  let  us  say, 
stopped  by  a  valve  which  refuses  passage  of  silver  from 
the  bullion  reservoir  to  the  money  reservoir  but  not 
the  reverse  (for  no  law  ever  can  prevent  the  melting 
down  of  silver  coins  into  bullion).  Newly  mined  silver 
cannot  now  become  money,  and  thus  lower  the  pur- 
chasing power  of  the  money. 

On  the  other  hand,  new  supplies  of  gold  continue  to 
affect  the  value  of  currency,  as  before,  —  the  value,  not 
only  of  the  gold,  but  also  of  the  concurrently  circulating 
overvalued  silver.  If  more  gold  should  flow  into  the 
money  reservoir,  it  would  raise  the  currency  level. 
Should  this  level  ever  become  higher  than  the  level 
of  the  silver  bullion  reservoir,  silver  would  flow  from 
the  money  reservoir  into  the  bullion  reservoir ;  for  the 


Sec.  4]  INFLUENCE   OF  MONETARY  SYSTEMS  129 

passage  in  that  direction  (i.e.  melting)  is  still  free. 
So  long,  however,  as  the  currency  level  is  below  the 
silver  level,  i.e.  so  long  as  the  coined  silver  is  worth 
more  than  the  uncoined,  there  will  be  no  flow  of  silver 
in  either  direction.  The  legal  prohibition  prevents 
the  flow  in  one  direction,  and  the  laws  of  relative  levels 
prevent  its  flow  in  the  other. 

In  the  case  just  discussed,  the  value  of  the  coined 
silver  will  be  equal  to  the  value  of  gold  at  the  legal  ratio. 
Precisely  the  same  principle  applies  in  the  case  of  any 
money,  the  coined  value  of  which  is  greater  than  the 
value  of  its  constituent  material.  Take  the  case,  for 
instance,  of  paper  money.  So  long  as  it  has  the  dis- 
tinctive characteristic  of  money, — general  acceptability 
at  its  legal  value,  —  and  is  limited  in  quantity,  its  value 
will  ordinarily  be  equal  to  that  of  its  legal  equivalent 
in  gold.  If  its  quantity  increases  indefinitely,  it  will 
gradually  push  out  all  the  gold  and  entirely  fill  the 
money  reservoir,  just  as  silver  would  do  under  bimetal- 
lism if  produced  in  sufficiently  large  amounts.  Like- 
wise, credit  money  and  credit  in  the  form  of  bank 
deposits  would  have  this  effect.  To  the  extent  that 
they  are  used,  they  lessen  the  demand  for  gold,  decrease 
its  value  as  money,  and  cause  more  of  it  to  go  into 
the  arts  or  to  other  countries. 

So  long  as  the  quantity  of  silver  or  other  token 
money,  e.g.  paper  money,  is  too  small  to  displace  gold 
completely,  gold  will  continue  in  circulation.  The  value 
of  the  other  money  in  this  case  cannot  fall  below  that 
of  gold.  For  if  it  should,  it  would,  by  Gresham's  Law, 
displace  gold,  which  we  have  supposed  it  is  not  of  suffi- 
cient quantity  to  do.  The  parity  between  silver  coin 
and  gold  under  the  "limping"  standard  is,  therefore, 
not  necessarily  dependent  on  any  redeemability  in  gold, 


130        THE    PURCHASING   POWER   OF  MONEY        [Chap.  Vll 

but  may  result  merely  from  limitation  in  the  amount  of 
silver  coin.  Such  limitation  is  usually  sufficient  to 
maintain  parity  despite  irredeemability.  This  is  not 
always  true,  however ;  for  if  the  people  should  lose  con- 
fidence in  some  form  of  irredeemable  paper  or  token 
money,  even  though  it  were  not  overissued,  it  would  de- 
preciate and  be  nearly  as  cheap  in  money  form  as  it  is  in 
the  raw  state.  A  man  is  willing  to  accept  money  at  its 
face  value  so  long  as  he  has  confidence  that  every  one 
else  is  ready  to  do  the  same.  But  it  is  possible,  for 
instance,  for  a  mere  fear  of  overissue  to  destroy  this 
confidence.  The  payee,  who,  under  ordinary  circum- 
stances, submits  patiently  to  whatever  money  is  cus- 
tomary or  legal  tender,  may  then  take  a  hand  and 
insist  on  ''contracting  out"  of  the  offending  standard.^ 
That  is,  he  may  insist  on  making  all  his  future  con- 
tracts in  terms  of  the  better  metal,  — -  gold,  for  instance, 
—  and  thus  contribute  to  the  further  downfall  of  the 
depreciated  paper. 

Irredeemable  paper  money,  then,  like  our  irredeemable 
silver  dollars,  may  circulate  at  par  with  other  money, 
if  limited  in  quantity  and  not  too  unpopular.  If  it 
is  gradually  increased  in   amount,    such   irredeemable 

*  In  the  mechanical  interpretation,  since  the  law  would  now  be 
inoperative,  the  film  would  no  longer  yield  to  pressure  from  the 
right,  and  an  appreciable  difference  of  level  on  its  two  sides  would 
ensue.  Such  a  mechanism  would  illustrate  the  concurrent  cir- 
culation of  two  metals  at  independent  valuations,  but  experience 
shows  that  such  a  condition  is  too  full  of  inconveniences  to  be 
maintained  long.  The  silver  will  be  progressively  tabooed,  that  is, 
its  velocity  of  circulation  will  gradually  decrease.  This,  as  we 
have  seen,  may  be  figured  by  supposing  the  currency  reservoir  (on 
the  right  of  the  film  only)  to  be  thickened,  thus  bringing  the  film 
to  the  right.  If  the  silver  is  completely  tabooed,  the  film  will  be 
completely  to  the  right,  and  there  will  be  gold  monometallism. 
The  monetary  result  of  such  discrimination  against  silver  is  thus 
the  appreciation  of  gold. 


Sec.  4]  INFLUENCE   OF  MONETARY   SYSTEMS  131 

money  may  expel  all  metallic  money  and  be  left  in 
undisputed  possession  of  the  field. 

But  though  such  a  result  —  a  condition  of  irredeem- 
able paper  money  as  the  sole  currency  —  is  possible,  it 
has  seldom  if  ever  proved  desirable.  Unless  safeguarded, 
irredeemability  is  a  constant  temptation  to  abuse,  and 
this  fact  alone  causes  business  distrust  and  discourages 
long-time  contracts  and  enterprises.  Irredeemable 
paper  money  has  almost  invariably  proved  a  curse  to 
the  country  employing  it.  While,  therefore,  redeema- 
bility  is  not  absolutely  essential  to  produce  parity  of 
value  with  the  primary  money,  practically  it  is  a  wise 
precaution.  The  lack  of  redeemability  of  silver  dollars 
in  the  United  States  is  one  of  the  chief  defects  in  our 
unsatisfactory  monetary  system,  and  a  continuing 
danger. 

It  is  possible  to  have  various  degrees  of  redeemability. 
One  of  the  most  interesting  systems  of  partial  redeem- 
ability is  the  system  now  known  as  the  gold-exchange 
standard,  by  which  countries,  not  themselves  on  a  strict 
gold  basis,  nevertheless  maintain  substantial  parity  with 
gold  through  the  foreign  exchanges.  By  this  system  the 
government  or  its  agent,  while  not  redeeming  its  cur- 
rency in  gold,  redeems  it  in  orders  on  gold  abroad. 
That  is,  the  government  sells  bills  of  exchange  on  Lon- 
don or  New  York  at  a  stated  price.  The  currency  which 
it  thus  receives,  and  in  a  sense  redeems,  it  keeps  out  of 
circulation  until  the  price  of  foreign  exchange  falls  {i.e. 
until  the  demand  for  redemption  ceases). 

The  gold-exchange  standard  may  be  regarded  as  a 
kind  of  limping  standard  with  the  added  feature  of 
partial  redemption. 

This  added  feature,  however,  greatly  modifies  the 
nature  of  the  limping  standard.     The  limping  standard 


132        THE    PURCHASING   POWER   OF  MONEY        [Chap.  VII 

without  the  gold-exchange  attachment  may  at  any  time 
break  down,  if  the  silver  (or  whatever  else  the  over- 
valued money  may  be)  should  become  so  redundant, 
relatively  to  trade,  as  completely  to  displace  gold.  As 
soon  as  all  gold  is  driven  abroad,  parity  with  gold  ceases. 
But  with  the  gold-exchange  system  this  catastrophe  is 
avoided.  In  fact,  with  this  system  it  is  not  necessary  to 
have  gold  in  circulation  at  any  time.  The  willingness  of 
the  government  to  sell  foreign  exchange  at  a  fixed  price, 
and  to  lock  up  the  silver  it  receives  thereby,  takes  that 
much  currency  out  of  circulation  just  as  effectively  as 
though  the  equivalent  of  gold  had  been  exported.  So 
long  as  the  government  is  willing  and  able  to  maintain 
the  price  of  bills  of  exchange  with  a  gold  country,  it, 
ipso  facto,  maintains  approximate  parity  with  gold.^ 


We  have  now  to  illustrate,  by  historical  examples,  the 
principles  just  explained.  The  first  and  most  important 
case  is  that  of  France.  The  ratio  of  15^  to  1  was 
adopted  by  France  in  1785  and  continued  by  the  law 
of  1803.  The  history  of  France  and  the  Latin  Union 
during  the  period  from  1785,  and  especially  from  1803, 
to  1873  is  instructive.  It  affords  a  practical  illustration 
of  the  theory  that  when  conditions  are  favorable,  gold 
and  silver  can  be  kept  tied  together  for  a  considerable 
period  by  means  of  bimetaUism.  During  this  period 
the  public  was  ordinarily  unconscious  of  any  disparity 
of  value,  and  only  observed  the  changes  from  the  rela- 
tive predominance  of  gold  to  the  relative  predominance 
of  silver  in  the  currency  and  vice  versa.  In  the  whole- 
sale bullion  market,  it  is  true,  there  were  slight  varia- 

1  Cf.  Charles  A.  Conant,  "  The  Gold  Exchange  Standard,"  Eco- 
nomic Journal,  June,  1909,  pp.  190-200. 


Sec.  5]  INFLUENCE    OF   MONETARY   SYSTEMS  133 

tions  from  the  ratio  of  162  to  1.     But  such  variations 
simply  supplied  the  force  to  restore  equilibrium. 

From  1803  until  about  1850  the  tendency  was  for 
silver  to  displace  gold.  In  our  mechanical  terms  there 
was,  for  the  most  part,  an  inflow  on  the  right-hand  side 
of  the  money  reservoir,  and  the  film  was  gradually 
pressed  leftward.  The  statistics  for  the  movements 
of  gold  and  silver  are  not  given  separately  and  continu- 
ously before  1830.  But  from  1830  to  1847,  inclusive, 
there  was  a  net  export  of  gold  of  73,000,000  francs, 
although  five  of  the  years  showed  an  import,  making 
an  average  export  of  over  4,000,000  francs  a  year.^ 
From  1830  until  1851  there  was  a  net  importation  of 
silver  in  every  year,  amounting  to  a  total  for  the  period 
of  2,297,000,000  francs  or  an  average  of  over  104,000,000 
francs  a  year.^  The  statistics  for  silver  are  taken  to 
1851  because  after  that  year  the  movement  for  silver 
was  reversed,  while  for  gold  the  inward  flow  began 
with  1848.  Silver  was  displacing  gold  and  filling  up 
the  currency  reservoir.  Nevertheless,  the  reservoir 
was  expanding  so  fast,  that  is,  trade  was  increasing,  that 
there  was  no  increase  of  prices,  but  rather  a  decrease. 
By  1850,  the  film  had  practically  reached  its  limit. 
Bimetallism  would  have  broken  down  and  resulted  in 
silver  monometallism  then  and  there,  except  for  the 
fact  that,  as  though  to  save  the  day,  gold  had  just  been 
discovered  in  California.  The  consequence  of  the  new 
and  increased  gold  production  was  a  reverse  movement, 
an  inflow  of  gold  into  the  French  currency  and  an  out- 
flow of  silver.  From  1848  to  1870,  inclusive,  the  net 
importation  of  gold  amounted  to  5,153,000,000  francs 
or  over  224,000,000  francs  a  year,  while  the  net  exporta- 

^  W.  A.  Shaw,  The  History  of  the  Currency,  3d  ed.,  London 
(Clement  Wilson),  1899,  p.  183.  2  j^^i^,,  p.  184. 


134        THE    PURCHASING   POWER   OF  MONET        [Chap.  VII 

tion  of  silver  from  1852  to  1864,  inclusive,  amounted  to 
1,726,000,000  francs  or  nearly  133,000,000  francs  a  year.^ 
Gold  was  displacing  silver  and  filling  the  currency.  It 
seemed  probable  that  France  would  be  entirely 
drained  of  her  silver  currency  and  come  to  a  gold  basis. 
France  formed  with  Belgium,  Italy,  and  Switzerland 
in  1865,  and  Greece  in  1868,  the  Latin  Monetary  Union. 
The  amount  of  silver  in  the  subsidiary  coins  was  re- 
duced, but  the  standard  silver  coins  were  kept  at  the  old 
ratio  with  gold.  But  the  new  gold  mines  were  gradu- 
ally exhausted,  while  silver  production  increased,  with 
the  consequence  that  there  was  again  a  reversal  of 
the  movement.  From  1871  to  1873,  inclusive,  the 
exportation  of  gold  netted  375,000,000  francs,  or  an 
average  of  125,000,000  francs  a  year,  while  from  1865 
to  1873,  inclusive,  the  net  importation  of  silver  was 
860,000,000  francs,  or  over  94,000,000  francs  a  year. 
Thus,  even  before  the  gold  began  to  flow  out,  in  1871, 
silver  had  begun  to  flow  in,  i.e.  in  1865.  Silver  grad- 
ually pushed  gold  out  of  circulation  and,  had  not  France 
and  the  other  countries  of  the  Latin  Union  successively 
suspended  the  free  coinage  of  silver  in  1873-1878,  they 
would  have  found  themselves  on  a  silver,  instead  of  a 
gold,  basis.  It  has  been  claimed  by  bimetallists  that 
this  action  in  demonetizing  silver  was  itself  the  cause  of 
the  breakdown.  The  truth  is,  that  the  breakdown 
was  the  cause  of  demonetization,  although  demonetiza- 
tion, by  keeping  back  silver  from  circulation  and  keeping 
gold  in  circulation,  did  operate  to  widen  the  breach 
already  made. 

The  film,  in  other  words,  was  close  to  the  left  limit,  and 
the  currency  reservoir  was  filled  for  the  most  part  with 

^  W.  A.   Shaw,   The   History  of  the   Currency,  3d  ed.,   London 
(Clement  Wilson),  1899,  pp.  183  and  184. 


Sec.  6]  INFLUENCE    OF   MONETARY   SYSTEMS  135 

silver.  The  Latin  Union  might  conceivably  have  main- 
tained bimetalHsm  longer  if  other  countries  had  joined 
with  them.  But  it  had  to  absorb,  not  only  much  of 
the  silver  provided  by  the  mines,  but  also  a  considerable 
amount  which  had  previously  formed  part  of  the  mon- 
etary stock  of  Germany  and  which,  at  the  adoption  of 
the  gold  standard  by  that  country  following  the  Franco- 
Prussian  War,  was  thrown  on  the  market.  That  is, 
not  only  silver  mines,  but  countries  demonetizing  silver, 
dumped  silver  on  the  Latin  Union.  Add  to  this  the 
movement  toward  the  gold  standard  in  Scandinavia 
and  the  United  States,  and  it  becomes  evident  that  the 
obstacles  were  many  for  a  union  comprising  so  few,  and 
mostly  unimportant,  states. 

The  parity  with  gold  of  the  silver  remaining  in  circu- 
lation in  the  Latin  Union  is  now  preserved  on  the  prin- 
ciples explained  earher  in  the  chapter,  viz.  by  limiting 
its  quantity,  as  well  as  by  making  it  full  legal  tender 
and  receivable  for  public  dues. 

§6 

It  is  strange  that  the  lessons  of  the  French  and  other 
experiments  do  not  seem  to  be  generally  understood 
either  by  monometallists  or  bimetaUists.  For  instance, 
uncompromising  monometallists  have  pointed  to  the 
variation  in  the  value  of  gold  and  silver  during  the  three 
quarters  of  a  century  as  disproving  the  possibility  of 
maintaining  a  legal  ratio.  They  might  as  well  point  to 
the  ripples  on  a  pond  or  the  slight  gradient  of  a  river, 
as  disproving  the  fact  that  water  seeks  a  level.  These 
ripples  are  really  evidence  of  the  process  of  seeking  a 
level  and  are  trifling  as  compared  with  those  which  in 
all  probability  would  have  taken  place  had  there  not 
been  a  legal  ratio.     The  diagram  and  tables  used  in 


136        THE    PURCHASING   POWER   OF  MONEY        [Chap.  Vii 

Shaw's  History  of  the  Currency  and  the  similar  diagram 
here  given  show  that  dm-ing  the  period  of  inflowing 
silver,  1803  to  1850,  in  spite  of  the  great  increase  in 
the  quantity  of  silver,  the  ratio  was  changed  from  15 J 
to  1  by  at  most  only  .75  points  or  slightly  over  4.8  per 
cent  in  any  year,  and  the  average  departure  was  only 
.29  points  or  1.9  per  cent.  Moreover,  the  greater  part  of 
the  deviation  is  explainable  by  the  seigniorage  charge 
then  in  force  in  France.^  During  the  succeeding  period 
from  1851  to  1870,  characterized  largely  by  an  inflow  of 
gold,  the  maximum  departure  (in  the  opposite  direction) 
was  .31  points  or  2  per  cent,  with  an  average  departure 
of  .14  points  or  .9  per  cent,  while  during  the  succeeding 
period  of  inflowing  silver  and  outflowing  gold,  from 
1871  to  1873,  the  ratio  rose  above  15i  to  1  by  a  maxi- 
mum of  .42  points  or  2.7  per  cent  and  an  average  of 
.21  points  or  1.4  per  cent.  Contrast  these  figures  with 
those  since  1873."  The  maximum  departure  from  the 
ratio  of  15J  to  1  since  1873  is  23.65  points,  or  152.6 
percent,  and  the  average  departure  10.4  points,  or  67.1 
per  cent.^  The  history  of  the  ratio  is  shown  in  Figure  9. 
On  the  other  hand,  bimetallists  have  often  failed  to 
see  that  this  experiment  illustrates  the  limits  as  well 
as  the  possibilities  of  bimetallism.  In  1850  bimetallism 
had  almost  broken  down  in  France  and  would  have  been 
succeeded  by  silver  monometallism  had  not  the  in- 
creased production  of  gold  reversed  the  flow.     In  1865, 

1  Cf.  J.  F.  Johnson,  Money  and  Currency,  Boston  (Ginn)  1905, 
p.  227. 

2  Although  France  did  not  entirely  suspend  the  coinage  of  the 
silver  five-franc  pieces  until  1876,  yet  limitation  began  with  1874. 
See  W.  A.  Shaw,  The  History  of  the  Currency,  pp.  194,  196. 

'  These  figures  are  compiled  from  data  given  in  W.  A.  Shaw, 
The  History  of  the  Currency,  p.  159,  and  Reports  of  the  Director  of  the 
Mint. 


Sec.  6] 


INFLUENCE    OF   MONETARY   SYSTEMS 


137 


gold  had  largely  driven  out  silver.  By  1873,  gold  had 
again  largely  disappeared,  and  it  seems  evident  that  it 
would  have  disappeared  entirely  had  not  the  suspension 
of  the  free  coinage  of  silver  followed.     A  continuance 


Hin!HMH'iWMiu,!'fr»i'!!H;Mi[[!lJiiliiniHlitHlHMnupu'iUHU<!HliHfHHimaaay^HtiiHHli!i-a!iiti^^ 


Fig.  9. 


of  bimetallism  at  a  ratio  of  15^  to  1  by  France  and  the 
Latin  Union  alone  would  doubtless  have  been  im- 
possible. Yet  the  attempt,  though  a  failure,  would  have 
kept  the  ratio  nearer  15|  to  1  than  it  actually  has  been; 


138        THE   PURCHASING   POWER   OF  MONEY        [Chap.  VII 

for  the  Union  would  have  furnished  a  large  market  for 
silver.  Possibly  bimetallism  could  have  been  main- 
tained longer,  despite  increased  silver  production,  had 
not  several  other  countries  adopted  the  gold  standard 
in  these  critical  years.  This  fact  helped  to  flood  the 
countries  of  the  Latin  Union  with  silver  and  drain  them 
of  their  gold.  These  countries  were  suffering  all  the 
expense  and  trouble  of  maintaining  the  ratio  between 
gold  and  silver,  while  other  countries  were  reaping  most 
of  the  benefits.  Herein  lies  one  of  the  weaknesses  of 
bimetallism  as  a  practical  political  proposition,  —  each 
country  prefers  that  some  other  country  or  countries 
should  be  the  ones  to  adopt  it.  There  is  little  prospect, 
therefore,  in  the  future,  of  any  single  country  taking  the 
initiative,  and  still  less  of  any  international  agreement. 

§  7 

The  system  now  in  use  in  France  is  also  employed 
in  many  other  countries  which,  like  France,  have  been 
forced  to  adopt  it  or  else  become  silver-standard  coun- 
tries. After  the  rupture  of  the  bimetallic  tie,  which 
until  1873  linked  all  gold  and  silver  countries  together, 
the  commercial  world  broke  into  two  parts,  gold-stand- 
ard countries  and  silver-standard  countries;  and  many 
desiring  to  join  the  ranks  of  the  former,  but  in  danger  of 
being  thrust  among  the  latter,  saved  themselves  by 
closing  their  mints  to  silver  and  thereby  adopting  the 
limping  standard.  One  of  these  countries  was  British 
India. 

The  case  of  India  is  interesting  because  it  never  was 
a  bimetallic  country,  and  at  the  time  of  the  adoption 
of  the  present  system,  in  which  gold  is  the  standard, 
no  gold  was  in  circulation.  The  mints  were  closed  to 
silver  in  June,  1893,  and  the  legal  ratio  put  the  rupee 


Sec.  7]  INFLUENCE   OF  MONETARY  SYSTEMS  139 

at  16c?.  At  first,  to  the  great  discomfiture  of  those 
who  had  advocated  the  new  system,  this  value  was 
not  maintained.  But  failure  at  first  was  to  be  ex- 
pected because  no  gold  was  in  circulation,  and  un- 
suspected coined  stores  of  silver  existed  to  swell  the 
circulation  in  spite  of  the  closure  of  the  mints.  More- 
over, the  government  accepted  from  banks  and  others 
considerable  amounts  of  silver  which  had  been  shipped 
to  India  before  the  closing  of  the  mints,  and  coined  it, 
and  a  considerable  amount  was  withdrawn  from  the 
government  reserve  and  put  into  circulation.  The 
value  of  the  rupee  fell  by  1895  to  as  low  as  ISd.  But 
even  from  the  first  the  value  of  the  rupee  kept  above 
the  value  of  its  contained  silver.  If  it  fell  as  compared 
with  the  then  appreciating  gold,  it  rose  as  compared 
with  the  value  of  silver  bullion.  Surely  this  may  be 
held  to  show  that  the  value  of  money  has  some  relation 
to  its  quantity,  apart  altogether  from  the  quantity  and 
the  value  of  the  constituent  material.  Furthermore, 
the  value  of  the  rupee  rose  gradually,  even  in  rela- 
tion to  the  gold  standard,  from  13d.  in  1895  to  15|  in 
1898  and  to  16d.,  the  legal  par,  by  1899,  where  it  has 
since  remained.  As  the  Indian  government  has,  during 
the  last  decade,  paid  out  rupees  for  gold  on  demand,  at 
this  rate,  the  value  of  the  rupee  cannot  go  appreciably 
higher.  Should  it  do  so,  gold  would  be  presented  for 
rupees,  more  rupees  would  have  to  be  issued,  and  this 
would  continue  until  their  value  had  fallen  to  IQd.  per 
rupee.^ 

The  system  of  India  is  virtually  the  gold-exchange 
standard  described  in  §  4.     The  same  system  is  now  in 

•  For  a  brief  history  and  discussion  of  the  Indian  experience, 
see  E.  W.  Kemmerer,  Money  and  Credit  Instruments  in  their  Relo' 
tion  to  Prices,  pp.  36-39. 


140        THE    PURCHASING   POWER   OF  MONEY        [Chap.  VII 

successful  operation  in  the  Philippines,  in  Mexico,  and 

in  Panama.^  It  withstood  a  severe  test  in  India  when, 
in  1908,  the  trade  balance  was  "adverse  "  and  required 
the  sale  of  over  £8,000,000  of  bills  on  London  be- 
fore the  Indian  currency  was  sufficiently  contracted  to 
stem  the  tide. 

§8 

Among  the  nations  which  now  have  the  limping 
standard  is  the  United  States.  In  1792,  Congress 
adopted  complete  bimetallism.  Full  legal-tender  qual- 
ity was  given  to  both  gold  and  silver  coins ;  both  were 
to  be  coined  freely  and  without  limit  at  the  ratio  of 
15  ounces  of  silver  to  1  of  gold. 

This  soon  came  to  be  below  the  market  ratio  as 
affected  by  conditions  abroad  and  especially  in  France. 
In  consequence,  gold  tended  to  leave  the  country.  It  is 
impossible  to  state  with  exactness  how  soon  this  move- 
ment began,  but  Professor  Laughlin  sets  it  as  early  as 
1810  and  concludes  that  by  1818  little  gold  was  in  cir- 
culation.2  America,  although  nominally  a  bimetallic 
country,  became  actually  a  silver  country. 

Influenced  partly  by  the  desire  to  bring  gold  back 
into  circulation,  and  partly  also,  perhaps,  by  the  sup- 
posed discoveries  of  gold  in  the  South,  Congress  passed 
acts  in  1834  and  1837  estabhshing  the  ratio  of  ''16  to 

^  See  Charles  A.  Conant,  "The  Gold  Exchange  Standard  in  the 
Light  of  Experience,"  Economic  Journal,  June,  1909,  pp.  190-200 ; 
Hanna,  Conant,  and  Jenks,  Report  on  the  Introduction  of  the  Gold  Ex- 
change Standard  into  China,  the  Philippine  Islands,  Panama,  and 
other  Silver-using  Countries  and  on  the  Stability  of  Exchange,  Wash- 
ington (Government  Printing  Office),  1904;  Kemraerer,  "Estab- 
lishment of  the  Gold  Exchange  Standard  in  the  Philippines," 
Quarterly  Journal  of  Economics,  August,  1905,  pp.  600-605. 

^  The  History  of  Biynetallism  in  the  United  States,  New  York 
(D.  Appleton  and  Company),  1901,  4th  ed.,  p.  29. 


Sec.  8]  INFLUENCE   OF  MONETARY  SYSTEMS  141 

1,"  —  or,  more  exactly,  16.002  to  1  in  1834  and  15.998 
to  1  in  1837.  Whereas  silver  money  had  been  over- 
valued by  the  previous  laws,  by  these  new  laws  gold 
was  overvalued.  That  is,  the  commercial  ratio  con- 
tinued to  be  near  15|  to  1,  while  the  monetary  ratio 
was  slightly  greater.  This  remained  the  case  up  to 
1850;  consequently,  in  accordance  with  Gresham's 
Law,  gold  money,  now  the  cheaper,  drove  out  silver 
money,  and  the  United  States  became  a  gold-standard 
country.  In  1853,  to  prevent  the  exportation  of  our 
subsidiary  silver  coins,  their  weight  was  reduced. 

The  United  States  continued  to  be  a  gold-using 
country  until  the  period  of  the  Civil  War,  during  which 
''greenbacks,"  or  United  States  notes,  were  issued  in 
considerable  excess.  Again  Gresham's  Law  came  into 
operation.  Gold  was  in  turn  driven  from  the  currency, 
and  the  United  States  came  to  a  paper  standard.^ 
For  some  years  after  the  close  of  the  war  the  country 
remained  on  a  paper  standard,  little  gold  being  in 
circulation  except  on  the  Pacific  coast,  and  not  much 
silver  anywhere. 

In  1873  Congress  passed  a  law  (called  by  bimetallists 
the  ''Crime  of  '73")  by  which  the  standard  silver  dollar 
was  entirely  omitted  from  the  list  of  authorized  coins. 

Of  course  this  could  not  have  had  any  immediate 
effect  on  the  value  of  gold  and  silver,  because  the  coun- 
try was  at  the  time  on  a  paper  basis.  But  when  specie 
payments  (i.e.  gold  and  silver  payments)  were  resumed 
in  1879,  this  repeal  of  the  free  coinage  of  silver  brought 
the  country  to  a  gold  standard,  not  to  a  silver  one. 

1  See  especially  Wesley  Clair  Mitchell,  History  of  the  Greenbacks, 
Chicago  (The  University  of  Chicago  Press),  1903 ;  also  his  Gold, 
Prices,  and  Wages  under  the  Greenback  Standard,  Berkeley,  California 
(University  of  California  Press),  1908. 


142         THE    PURCHASING   POWER    OF   MONEY         [Chap.  VII 

Had  it  not  been  for  the  law  of  1873,  the  United  States, 
when  it  returned  in  1879  to  a  metalHc  basis,  would  have 
been  a  silver  country  with  a  standard  considerably 
below  the  gold  standard  it  actually  reached.  Our 
monetary  problems  would  then  have  been  very  different 
from  what  they  actually  became. 

But  in  returning  to  a  gold  basis  we  reintroduced 
the  silver  dollar  in  a  minor  role.  Although  the  free 
coinage  of  silver  was  not  resumed,  the  advocates  of 
silver,  through  the  " Bland- AlUson  Act"  of  1878  and 
the  "Sherman  Act"  of  1890,  which  replaced  it,  succeeded 
in  pledging  the  government  to  the  purchase  of  large, 
but  not  unlimited,  amounts  of  silver  and  the  coinage 
of  a  large,  but  not  unlimited,  number  of  silver  dollars. 
The  Bland-Allison  Act  required  the  Secretary  of  the 
Treasury  to  purchase  every  month  from  $2,000,000  to 
$4,000,000  worth  of  silver  and  to  coin  it  into  standard 
silver  dollars.  The  Sherman  Act  required  the  pur- 
chase every  month  of  4,500,000  ounces  of  silver. 

Under  these  acts  554,000,000  silver  dollars  were 
coined,  although  less  than  20  per  cent  of  them  have 
ever  been  in  actual  circulation.  Silver  certificates 
redeemable  in  silver  dollars  on  demand,  and,  for  a  time 
treasury  notes,  have  circulated  in  the  place  of  this 
immense  mass  of  silver.  The  silver  dollars  (and  there- 
fore the  silver  certificates)  maintain  their  value  on 
a  parity  with  gold  primarily  because  they  are  limited 
in  amount.  If  any  question  were  raised  as  to  their 
parity  with  gold,  the  treasury  would  probably  offer  to 
specifically  redeem  them  in  gold.  No  law  directly 
provides  for  the  redemption  of  silver  in  gold,  but 
it  is  made  the  duty^  of  the  Secretary  of  the  Treasury 
to  take  such  measures  as  will  maintain  its  parity 
with  gold. 


Sec.  9]  INFLUENCE    OF   MONETARY   SYSTEMS  143 

In  1893  the  Sherman  Act  was  repealed,  and  in  1900 
a  law  was  passed  specifically  declaring  that  the  United 
States  shall  be  on  a  gold  basis. 

§9 

The  system  of  the  limping  standard,  now  obtaining 
in  the  United  States,  logically  forms  a  connecting  link 
between  complete  bimetallism  and  those  "composite" 
systems  by  which  any  number  of  different  kinds  of 
money  may  be  simultaneously  kept  in  circulation.  The 
manner  in  which  most  modern  civilized  states  have 
solved  the  problem  of  concurrent  circulation  has  been 
to  use  gold  as  a  standard,  and  to  use  silver,  nickel,  and 
copper  chiefly  as  subsidiary  money,  limited  in  quantity, 
with,  in  most  cases,  limited  amounts  of  paper  money, 
the  latter  being  usually  redeemable.  The  possible 
variations  of  this  composite  system  are  unlimited. 
In  the  United  States  at  present  we  have  a  system 
which  is  very  complicated  and  objectionable  in  many 
of  its  features  —  especially  (as  we  shall  presently  see) 
in  its  lack  of  elasticity.  Gold  is  the  standard  and  is 
freely  coined.  A  limited  number  of  silver  dollars, 
worth,  moneywise,  more  than  double  their  value  bullion- 
wise,  are  a  heritage  of  former  bimetallic  laws  long 
since  rendered  inoperative  by  the  paper  money  of  the 
Civil  War  and  expressly  repealed  in  1873.  The  two 
attempts  of  1878  and  1890  to  return  halfway  to  bi- 
metallism by  the  purchase  of  silver  —  attempts  dis- 
continued in  1893  —  have  greatly  swollen  the  volume 
of  coined  silver.  The  attempt  to  force  silver  dollars 
into  circulation  was  not  acceptable  to  the  business 
world,  and  Congress  therefore  issued  instead  the  two 
forms  of  paper  mentioned.  The  chief  form  is  the 
"silver  certificate."     For  each  silver  certificate  a  silver 


144         THE    PURCHASING    POWER   OF   MONEY        [Chap.  VII 

dollar  is  kept  in  the  vaults  of  the  United  States  gov- 
ernment. 

The  absurdity  of  the  situation  consists  in  the  fiction 
that  somehow  the  silver  keeps  paper  at  par  with  gold. 
The  paper  would  keep  its  parity  with  gold  just  as  well 
if  there  were  no  silver.  A  silver  dollar  as  silver  is  worth 
less  than  a  gold  dollar  just  as  truly  as  a  paper  dollar, 
as  paper,  is  worth  less  than  a  gold  dollar.  The  fact 
that  the  silver  is  worth  more  than  the  paper  will  not 
avail  in  the  least  to  make  the  paper  worth  a  whole 
dollar  so  long  as  the  silver  is  not  itself  worth  a  whole 
dollar.  A  pillar  which  reaches  only  halfway  to  the 
ceiling  cannot  hold  the  ceiling  up  any  more  than  a 
pillar  an  inch  high. 

The  paper  representatives  of  silver  would  continue 
to  circulate  as  well  as  they  do  now,  even  if  the  "  silver 
behind  them"  were  nonexistent,  although  the  absurdity 
of  the  situation  would  then  be  so  apparent  that  they 
would  probably  be  retired.  Whether  the  half  billion 
dollars  of  new  currency,  which  came  into  circulation 
with  the  Bland  and  Sherman  Acts,  are  of  silver,  over- 
valued to  the  extent  of  50  per  cent,  or  of  paper,  over- 
valued to  the  extent  of  100  per  cent,  does  not  really 
affect  the  principle  of  the  limping  standard  which  keeps 
silver  dollars  at  par  with  gold.  The  idle  silver  in  the 
treasury  vaults  represents  mere  waste,  a  subsidy  given 
by  the  government  to  encourage  silver  mining.  Its 
only  real  effect  to-day  is  to  mislead  the  public  into 
the  belief  that  in  some  way  it  keeps  or  helps  to  keep 
silver  certificates  at  par  with  gold;^  whereas  they  are 
kept  at  par  by  the   limitation  on   its   amount.     The 

1  Seager,  in  his  Introduction  to  Economics,  3d  ed.,  New  York  (Holt), 
1908,  p.  317,  urges  that  the  government  should  attempt  gradually 
to  dispose  of  this  silver  and  substitute  an  equal  value  of  gold. 


Sec.  9]  INFLUENCE    OF   MONETARY   SYSTEMS  145 

silver  and  its  paper  representatives  cannot  fall  below 
par  without  displacing  gold,  and  they  cannot  displace 
gold  because  there  are  not  enough  of  them. 

Another  and  equally  useless  anomaly  is  the  existing 
volume  of  ''greenbacks."  These  are  United  States 
government  notes.  Under  the  law  of  1875,  the  green- 
backs were  by  1879  retired  in  sufficient  numbers  to 
restore  parity  with  gold ;  but  by  a  counterlaw  of  1878, 
347,000,000  of  them  were  kept  in  circulation  and  are 
in  circulation  now.  As  soon  as  redeemed,  they  must 
be  reissued ;  they  cannot  be  retired.  They  are  a  fixed 
ingredient  in  our  money  pot  pourri,  neither  expansive 
nor  shrinkable.  They  have  been  kept  at  par  with  gold 
because  :  (1)  they  are  limited  in  amount ;  (2)  they  are 
redeemable  in  gold  on  demand ;  (3)  they  are  receivable 
for  taxes  and  are  legal  tender.  But  it  is  absurd  to 
redeem  but  not  retire  —  in  fact,  almost  a  contradiction 
in  terms.  This  absurdity  has  at  times  seriously  embar- 
rassed the  government. 

The  next  feature  of  our  currency  to  be  considered 
is  the  bank  note.  Although  the  National  Bank  acts 
wiped  out  the  old,  ill-assorted  state  bank  notes,  they  tied 
the  new  notes  up  with  the  war  debt,  and  they  have  re- 
mained so  tied  ever  since,  in  spite  of  the  fact  that  the 
advantages  of  the  connection  have  long  been  terminated 
and  the  disadvantages  have  grown  acute.  National 
bank  notes  cannot  legally  be  issued  in  excess  of  the 
government  debt,  however  urgent  the  need  for  them; 
nor  can  the  government  pay  its  debt  without  thereby 
compelling  national  banks  to  cancel  their  notes. 

One  of  the  curious  anomalies  of  the  situation  is  that 
the  prices  of  United  States  bonds  are  so  high,  and 
therefore  the  rate  of  interest  returned  on  these  bonds  so 
low  that  there  is  actually  less  inducement  to  issue  bank 


146         THE    PURCHASING    POWER   OF   MONEY         [Chap.  VII 

notes  in  regions  where  the  rate  of  interest  is  high,  as  in 
the  West,  than  in  regions  where  it  is  low,  as  in  the  East. 

The  result  is  an  inelastic  currency  which,  instead  of 
adjusting  itself  to  the  seasonal  fluctuations  in  trade, 
and  thus  mitigating  the  ensuing  variations  in  the  price 
level,  remains  a  hard  and  solid  mass  to  which  the  other 
elements  in  the  equation  of  exchange  must  adapt 
themselves.^ 

The  remaining  features  of  our  currency  system,  such 
as  fractional  and  minor  coins,  adjusted  to  public 
demand,  are  satisfactory.  The  gold  and  currency 
certificates  of  deposit  are  scarcely  independent  features, 
as  they  are  simply  government  receipts  for  public  con- 
venience representing  the  deposit  of  gold  or  greenbacks. 

The  status  in  the  United  States  July  1,  1912,  is 
represented  in  the  table  on  the  opposite  page  taken 
from  Comptrollers'  Reports  and  Treasurers'  Reports. 

We  see  here  a  currency  system  in  which  gold,  the 
basis  of  it  all,  enters  as  between  one  third  and  one  half 
the  circulation  outside  of  the  Treasury  and  banks  and 
a  little  over  half  the  money  in  banks  used  as  reserves 
for  deposits  (and  for  bank  notes,  though  these  are  also 
guaranteed  by  the  government).  The  remaining  money 
in  circulation  consists  almost  wholly  of  inelastic  and 
almost  constant  elements.  Consequently,  a  change  in 
the  quantity  of  gold  in  circulation  will  not  cause  a  pro- 
portional change  in  the  quantity  of  all  money  in  circu- 
lation, but  only  about  one  third  as  much.  Since, 
however,  almost  all  the  money  can  be  used  as  bank 
reserves,  even  national  bank  notes  being  so  used  by 
state  banks  and  trust  companies,   the  proportionate 

1  The  Aldrich-Vreeland  Act  of  1908  has  not  changed  this  situa- 
tion. However  helpful  it  may  be  in  mitigating  the  evils  of  crises,  it 
does  not  give  elasticity  of  the  currency  in  ordinary  times. 


Sec.  9] 


INFLUENCE   OF  MONETARY  SYSTEMS 


147 


relations  between  money  in  circulation,  money  in  re- 
serves, and  bank  deposits  will  hold  true  approximately 
as  the  normal  condition  of  affairs.  The  legal  require- 
ments as  to  reserves  strengthen  the  tendency  to  pre- 
serve such  a  relationship. 


Money  in  the  United  States  (in  Millions) 


Gold 

Silver 

U.S. 
Notes 

Bank 

Notes 

Subsidiary 

AND  Minor 

Coins 

Total 

In  U.S.  Treasury    . 
In  banks     .... 
Outside  both  .     .    . 

2641 
8012 
752  3 

26^ 
217 « 
323 

9 
253 

85 

40 
108 
597 

26 

38 

107 

365 
1417 
1864 

Total       .... 

1817 

566 

347 

745 

171 

3646 

In  the  United  States,  then,  we  have  a  currency  sys- 
tem in  which,  as  has  been  observed,  the  only  really 
adjustable  money  is  gold.  As  gold  requires  time  for 
minting  or  transportation,  the  adjustment  is  slow  and 
clumsy  as  compared  with  the  prompt  issue  or  retirement 
of  bank  notes  practiced  in  other  countries.  The  seasonal 
changes  in  the  purchasing  power  of  money,  as  well  as 
the  changes  connected  with  crises  and  credit  cycles,  are 

^  "  Free  "  gold  {i.e.  exclusive  of  gold  held  in  Treasury  for  gold 
certificates  held  by  the  public) . 

-  Including  563  millions  of  gold  certificates  for  which  gold  was 
on  deposit  in  the  United  States  government  vaults. 

'  Including  380  millions  of  gold  certificates  for  which  gold  was 
on  deposit  in  the  United  States  government  vaults. 

*  "Free"  {i.e.  exclusive  of  silver  held  in  the  Treasury  for  silver 
certificates  held  by  the  public) . 

^  Including  194  millions  of  silver  certificates  for  which  silver  was 
on  deposit  in  the  United  States  government  vaults. 

*  Including  275  millions  of  silver  certificates  for  which  silver  was 
on  deposit  in  the  United  States  government  vaults. 


148         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VII 

therefore  greatly  and  needlessly  aggravated.  As  this 
second  edition  goes  to  press,  there  seems  a  likelihood 
that  Congress  may  at  last  enact  legislation  designed  to 
remedy  this  condition. 


CHAPTER  VIII 

INFLUENCE    OF    QUANTITY   OP    MONEY   AND    OTHER   FAC- 
TORS  ON   PURCHASING   POWER   AND   ON   EACH   OTHER 

§1 

The  chief  purpose  of  the  foregoing  chapters  is 
to  set  forth  the  causes  determining  the  purchasing 
power  of  money.  This  purchasing  power  has  been 
studied  as  the  effect  of  five,  and  only  five,  groups  of 
causes.  The  five  groups  are  money,  deposits,  their  veloc- 
ities of  circulation,  and  the  volume  of  trade.  These 
and  their  effects,  prices,  we  saw  to  be  connected 
by  an  equation  called  the  equation  of  exchange, 
MV+  M'V  =  2pQ.  The  five  causes,  in  turn,  we  found 
to  be  themselves  effects  of  antecedent  causes  lying  en- 
tirely outside  of  the  equation  of  exchange,  as  follows : 
the  volume  of  trade  will  be  increased,  and  therefore 
the  price  level  correspondingly  decreased  by  the  dif- 
ferentiation of  human  wants ;  by  diversification  of  in- 
dustry; and  by  facilitation  of  transportation.  The 
velocities  of  circulation  will  be  increased,  and  there- 
fore also  the  price  level  increased  by  improvident 
habits ;  by  the  use  of  book  credit;  and  by  rapid  trans- 
portation. The  quantity  of  money  will  be  increased, 
and  therefore  the  price  level  increased  correspondingly 
(2  by  the  import  and  minting  of  money,  and,  anteced- 
ently, by  the  mining  of  the  money  metal ;  by  the 
introduction  of  another  and  initially  cheaper  money 
metal  through  bimetallism ;   and  by  the  issue  of  bank 

149    V 


150         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VIU 

notes   and  other  paper  money.      The  quantity  of  de- 
posits will  be  increased,  and  therefore  the  price  level- 
increased  by  extension  of  the  banking  system  and  by' 
the  use  of  book  credit.      The  reverse  causes  produce,  of 
course,  reverse  effects. 

Thus,  behind  the  five  sets  of  causes  which  alone 
affect  the  purchasing  power  of  money,  we  find  over  a 
dozen  antecedent  causes.  If  we  chose  to  pursue  the 
inquiry  to  still  remoter  stages,  the  number  of  causes 
would  be  found  to  increase  at  each  stage  in  much  the 
same  way  as  the  number  of  one's  ancestors  increases 
with  each  generation  into  the  past.  In  the  last  analysis 
myriads  of  factors  play  upon  the  purchasing  power  of 
money;  but  it  would  be  neither  feasible  nor  profitable 
to  catalogue  them.  The  value  of  our  analysis  consists 
rather  in  simplifying  the  problem  by  setting  forth 
clearly  the  five  proximate  causes  through  which  all 
others  whatsoever  must  operate.  At  the  close  of  our 
study,  as  at  the  beginning,  stands  forth  the  equation  of 
exchange  as  the  great  determinant  of  the  purchasing 
power  of  money.  With  its  aid  we  see  that  normally  the 
quantity  of  deposit  currency  varies  directly  with  the 
quantity  of  money,  and  that  therefore  the  introduction 
of  deposits  does  not  disturb  the  relations  we  found  to 
hold  true  before.  That  is,  it  is  still  true  that  (1)  prices 
vary  directly  as  the  quantity  of  money,  provided  the 
volume  of  trade  and  the  velocities  of  circulation  remain 
unchanged ;  (2)  that  prices  vary  directly  as  the  veloci- 
ties of  circulation  (if  these  velocities  vary  together), 
provided  the  quantity  of  money  and  the  volume  of 
trade  remain  unchanged;  and  (3)  that  prices  vary 
inversely  as  the  volume  of  trade,  provided  the  quantity 
of  money  —  and  therefore  deposits  —  and  their  ve- 
locities remain  unchanged. 


Sec.  2]  QUANTITY  THEORY  151 

§2 

It  is  proposed  in  this  chapter  to  inquire  how  far  these 
propositions  are  really  causal  propositions.  We  shall 
study  in  detail  the  influence  of  each  of  the  six  magni- 
tudes on  each  of  the  other  five.  This  study  will  afford 
answers  to  the  objections  which  have  often  been  raised 
to  the  quantity  theory  of  money. 

To  set  forth  all  the  facts  and  possibilities  as  to  causa- 
tion we  need  to  study  the  effects  of  varying,  one  at  a 
time,  the  various  magnitudes  in  the  equation  of  ex- 
change. We  shall  in  each  case  distinguish  between  the 
effects  during  transition  periods  and  the  ultimate  or 
normal  effects  after  the  transition  periods  are  finished. 
For  simplicity  we  shall  in  each  case  consider  the  normal 
or  ultimate  effects  first  and  afterward  the  abnormal  or 
transitional  effects. 

Since  almost  all  of  the  possible  effects  of  changes  in 
the  elements  of  the  equation  of  exchange  have  been 
already  set  forth  in  previous  chapters,  our  task  in  this 
chapter  is  chiefly  one  of  review  and  rearrangement. 

Our  first  question  therefore  is :  given  (say)  a  doubling 
of  the  quantity  of  money  in  circulation  {M),  what  are 
the  normal  or  ultimate  effects  on  the  other  magnitudes 
in  the  equation  of  exchange,  viz. :  M\  V,  V,  the  p's 
and  the  Q's  ? 

We  have  seen,  in  Chapter  III,  that  normally  the  effect 
of  doubling  money  in  circulation  {M)  is  to  double 
deposits  {M')  because  under  any  given  conditions  of 
industry  and  civilization  deposits  tend  to  hold  a  fixed  or 
normal  ratio  to  money  in  circulation.  Hence  the  ulti- 
mate effect  of  a  doubhng  in  M  is  the  same  as  that  of  dou- 
bling both  M  and  M'.  We  propose  next  to  show  that  this 
doubling  of  M  and  M'  does  not  normally  change  V,  V  or 


152         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VIII 

the  Q's,  but  only  the  p's.     The  equation  of  exchange  of 
itself  does  not  affirm  or  deny  these  propositions. 

For  aught  the  equation  of  exchange  itself  tells  us, 
the  quantities  of  money  and  deposits  might  even  vary 
inversely  as  their  respective  velocities  of  circulation. 
Were  this  true,  an  increase  in  the  quantity  of  money 
would  exhaust  all  its  effects  in  reducing  the  velocity  of 
circulation,  and  could  not  produce  any  effect  on  prices. 
If  the  opponents  of  the  "quantity  theory"  could  estabhsh 
such  a  relationship,  they  would  have  proven  their  case 
despite  the  equation  of  exchange.  But  they  have  not 
even  attempted  to  prove  such  a  proposition.  As  a 
matter  of  fact,  the  velocities  of  circulation  of  money 
and  of  deposits  depend,  as  we  have  seen,  on  technical 
conditions  and  bear  no  discoverable  relation  to  the 
quantity  of  money  in  circulation.  Velocity  of  circula- 
tion is  the  average  rate  of  "turnover,"  and  depends  on 
countless  individual  rates  of  turnover.  These,  as  we 
have  seen,  depend  on  individual  habits.  Each  person 
regulates  his  turnover  to  suit  his  convenience.  A 
given  rate  of  turnover  for  any  person  implies  a  given 
time  of  turnover  —  that  is,  an  average  length  of  time  a 
dollar  remains  in  his  hands.  He  adjusts  this  time  of 
turnover  by  adjusting  his  average  quantity  of  pocket 
money,  or  till  money,  to  suit  his  expenditures.  He 
will  try  to  avoid  carrying  too  little  lest,  on  occasion, 
he  be  unduly  embarrassed;  and  on  the  other  hand 
to  avoid  encumbrance,  waste  of  interest,  and  risk 
of  robbery,  he  will  avoid  carrying  too  much.  Each 
man's  adjustment  is,  of  course,  somewhat  rough,  and 
dependent  largely  on  the  accident  of  the  moment; 
but,  in  the  long  run  and  for  a  large  number  of  people, 
the  average  rate  of  turnover,  or  what  amounts  to 
the  same  thing,  the  average  time  money  remains  in 


Sec.  2]  QUANTITY   THEORY  163 

the  same  hands,  will  be  very  closely  determined.  It 
will  depend  on  density  of  population,  commercial  cus- 
toms, rapidity  of  transport,  and  other  technical  condi- 
tions, but  not  on  the  quantity  of  money  and  deposits 
nor  on  the  price  level.  These  may  change  without  any 
effect  on  velocity.  If  the  quantities  of  money  and  de- 
posits are  doubled,  there  is  nothing,  so  far  as  velocity  of 
circulation  is  concerned,  to  prevent  the  price  level  from 
doubUng.  On  the  contrary,  doubling  money,  deposits, 
and  prices  would  necessarily  leave  velocity  quite  un- 
changed. Each  individual  would  need  to  spend  more 
money  for  the  same  goods,  and  to  keep  more  on  hand. 
The  ratio  of  money  expended  to  money  on  hand  would 
not  vary.  If  the  number  of  dollars  in  circulation  and 
in  deposit  should  be  doubled  and  a  dollar  should  come 
to  have  only  half  its  former  purchasing  power,  the 
change  would  imply  merely  that  twice  as  many  dollars 
as  before  were  expended  by  each  person  and  twice  as  ' 
many  kept  on  hand.  The  ratio  of  expenditure  to  stock 
on  hand  would  be  unaffected. 

If  it  be  objected  that  this  assumes  that  with  the 
doubling  in  M  and  M'  there  would  be  also  a  doubling 
of  prices,  we  may  meet  the  objection  by  putting  the 
argument  in  a  slightly  different  form.  Suppose,  for  a 
moment,  that  a  doubling  in  the  currency  in  circulation 
should  not  at  once  raise  prices,  but  should  halve  the  ve- 
locities instead ;  such  a  result  would  evidently  upset  for 
each  individual  the  adjustment  which  he  had  made  of 
cash  on  hand.  Prices  being  unchanged,  he  now  has 
double  the  amount  of  money  and  deposits  which  his  ^ 

convenience  had  taught  him  to  keep  on  hand.     He  will       \     ^ 
then  try  to  get  rid  of  the  surplus  money  and  deposits  by      V    v 
buying  goods.     But  as  somebody  else  must  be  found  to  l^?^^v 
take  the  money  off  his  hands,  its  mere  transfer  will  not        Jj 


154         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VIII 

diminish  the  amount  in  the  community.  It  will  sim- 
ply increase  somebody  else's  surplus.  Everybody  has 
money  on  his  hands  beyond  what  experience  and  con- 
venience have  shown  to  be  necessary.  Everybody  will 
want  to  exchange  this  relatively  useless  extra  money 
for  goods,  and  the  desire  so  to  do  must  surely  drive  up 
the  price  of  goods.  No  one  can  deny  that  the  effect  of 
every  one's  desiring  to  spend  more  money  will  be  to 
raise  prices.  Obviously  this  tendency  will  continue 
until  there  is  found  another  adjustment  of  quantities 
to  expenditures,  and  the  F's  are  the  same  as  originally. 
That  is,  if  there  is  no  change  in  the  quantities  sold 
(the  Q's),  the  only  possible  effect  of  doubling  M  and  M' 
will  be  a  doubling  of  the  p's  ;  for  we  have  just  seen  that 
the  y's  cannot  be  permanently  reduced  without  causing 
people  to  have  surplus  money  and  deposits,  and  there 
cannot  be  surplus  money  and  deposits  without  a  desire 
to  spend  it,  and  there  cannot  be  a  desire  to  spend  it 
without  a  rise  in  prices.  In  short,  the  only  way  to  get  rid 
of  a  plethora  of  money  is  to  raise  prices  to  correspond. 

So  far  as  the  surplus  deposits  are  concerned,  there 
might  seem  to  be  a  way  of  getting  rid  of  them  by  can- 
celing bank  loans,  but  this  would  reduce  the  normal 
ratio  which  M'  bears  to  M,  which  we  have  seen  tends 
to  be  maintained. 

We  come  back  to  the  conclusion  that  the  velocity  of 
circulation  either  of  money  or  deposits  is  independent 
of  the  quantity  of  money  or  of  deposits.  No  reason  has 
been,  or,  so  far  as  is  apparent,  can  be  assigned,  to  show 
why  the  velocity  of  circulation  of  money,  or  deposits, 
should  be  different,  when  the  quantity  of  money,  or 
deposits,  is  great,  from  what  it  is  when  the  quantity 
is  small. 

There  still  remains  one  seeming  way  of  escape  from 


Sec.  2J  QUANTITY  THEORY  155 

the  conclusion  that  the  sole  effect  of  an  increase  in  the 
quantity  of  money  in  circulation  will  be  to  increase 
prices.  It  may  be  claimed  —  in  fact  it  has  been  claimed 
—  that  such  an  increase  results  in  an  increased  volume 
of  trade.  We  now  proceed  to  show  that  (except  during 
transition  periods)  the  volume  of  trade,  like  the  velocity 
of  circulation  of  money,  is  independent  of  the  quantity 
of  money.  An  inflation  of  the  currency  cannot  increase 
the  product  of  farms  and  factories,  nor  the  speed  of 
freight  trains  or  ships.  The  stream  of  business  depends 
on  natural  resources  and  technical  conditions,  not  on 
the  quantity  of  money.  The  whole  machinery  of  pro- 
duction, transportation,  and  sale  is  a  matter  of  physical 
capacities  and  technique,  none  of  which  depend  on  the 
quantity  of  money.  The  only  way  in  which  the  quan- 
tities of  trade  appear  to  be  affected  by  the  quantity  of 
money  is  by  influencing  trades  accessory  to  the  creation 
of  money  and  to  the  money  metal.  An  increase  of  gold 
money  will,  as  has  been  noted,  bring  with  it  an  increase 
in  the  trade  in  gold  objects.  It  will  also  bring  about 
an  increase  in  the  sales  of  gold  mining  machinery,  in 
gold  miners'  services,  in  assaying  apparatus  and  labor. 
These  changes  may  entail  changes  in  associated  trades. 
Thus  if  more  gold  ornaments  are  sold,  fewer  silver  orna- 
ments and  diamonds  may  be  sold.  Again  the  issue  of 
paper  money  may  affect  the  paper  and  printing  trades, 
the  employment  of  bank  and  government  clerks,  etc. 
In  fact,  there  is  no  end  to  the  minute  changes  in  the  Q's 
which  the  changes  mentioned,  and  others,  might  bring 
about.  But  from  a  practical  or  statistical  point  of  view 
they  amount  to  nothing,  for  they  could  not  add  to  nor 
subtract  one  tenth  of  1  per  cent  from  the  general  aggre- 
gate of  trade.  Only  a  very  few  Q's  would  be  appre- 
ciably affected,  and  those  few  very  insignificant.    Prob- 


156        THE    PURCHASING   POWER   OF  MONEY       [Chap.  VIII 

ably  no  one  will  deny  this,  but  some  objectors  might 
claim  that,  though  technique  of  production  and  trade  de- 
termine most  of  these  things,  nevertheless  the  Q's  —  the 
actual  quantities  of  goods  exchanged  for  money  and  deposit 
currency  —  might  conceivably  vary  according  as  barter 
is  or  is  not  resorted  to.  If  barter  were  as  convenient 
as  sale-and-purchase,  this  contention  would  have  force. 
There  would  then  be  little  need  of  distinguishing  be- 
tween money  as  the  generally  acceptable  medium  of  ex- 
change and  other  property  as  not  generally  acceptable. 
If  all  property  were  equally  acceptable,  all  property 
would  be  equally  money  ;  or  if  there  were  many  kinds  of 
property  nearly  as  exchangeable  as  money,  resort  to 
barter  would  be  so  easy  that  some  of  the  goods  sold  for 
money  could  be  almost  equally  well  bartered  for  some- 
thing else.  But  as  long  as  there  were  any  preference 
at  all  for  the  use  of  money,  resort  to  barter  would  be 
reluctantly  made  and  as  a  temporary  expedient  only. 
We  have  seen  this  when  studying  transition  periods. 
Under  normal  conditions  and  in  the  long  run  only  a 
negligible  fraction  of  modern  trade  can  be  done  through 
barter.  We  conclude,  therefore,  that  a  change  in  the 
quantity  of  money  will  not  appreciably  affect  the  quanti- 
ties of  goods  sold  for  money. 

Since,  then,  a  doubling  in  the  quantity  of  money: 
(1)  will  normally  double  deposits  subject  to  check  in  the 
same  ratio,  and  (2)  will  not  appreciably  affect  either  the 
velocity  of  circulation  of  money  or  of  deposits  or  the  vol- 
ume of  trade,  it  follows  necessarily  and  mathematically 
that  the  level  of  prices  must  double.  While,  therefore, 
the  equation  of  exchange,  of  itself,  asserts  no  causal 
relations  between  quantity  of  money  and  price  level, 
any  more  than  it  asserts  a  causal  relation  between  any 
other  two  factors,  yet,  when  we  take  into  account  con- 


Sec.  2]  QUANTITY   THEORY  157 

ditions  known  quite  apart  from  that  equation,  viz., 
that  a  change  in  M  produces  a  proportional  change  in 
M',  and  no  changes  in  V,  V\  or  the  Q's,  there  is  no  pos- 
sible escape  from  the  conclusion  that  a  change  in  the 
quantity  of  money  (M)  must  normally  cause  a  propor- 
tional change  in  the  price  level  (the  p's). 

One  of  the  objectors  to  the  quantity  theory  attempts 
to  dispose  of  the  equation  of  exchange  as  stated  by 
Newcomb,  by  calling  it  a  mere  truism.  While  the 
equation  of  exchange  is,  if  we  choose,  a  mere  "truism," 
based  on  the  equivalence,  in  all  purchases,  of  the  money 
or  checks  expended,  on  the  one  hand,  and  what  they 
buy,  on  the  other,  yet  in  view  of  supplementary 
knowledge  as  to  the  relation  of  M  to  M ',  and  the  non- 
relation  of  M  to  V,  V,  and  the  Q's,  this  equation  is 
the  means  of  demonstrating  the  fact  that  normally 
the  p's  vary  directly  as  M,  that  is,  demonstrating  the 
quantity  theory.  ''Truisms"  should  never  be  neg- 
lected. The  greatest  generalizations  of  physical  science, 
such  as  that  forces  are  proportional  to  mass  and  ac- 
celeration, are  truisms,  but,  when  duly  supplemented 
by  specific  data,  these  truisms  are  the  most  fruitful 
sources  of  useful  mechanical  knowledge.  To  throw 
away  contemptuously  the  equation  of  exchange  because 
it  is  so  obviously  true  is  to  neglect  the  chance  to  formu- 
late for  economic  science  some  of  the  most  important 
and  exact  laws  of  which  it  is  capable. 

We  may  now  restate,  then,  in  what  causal  sense  the 
quantity  theory  is  true.  It  is  true  in  the  sense  that  one 
of  the  normal  effects  of  an  increase  in  the  quantity  of  money 
is  an  exactly  proportional  increase  in  the  general  level  of 
prices.^ 

'  Cf .  Albert  Aupetit,  Essai  sur  la  theorie  generale  de  la  monnaie, 
Paris  (Guillaumin),  1901. 


y' 


158        THE    PURCHASING   POWER  OF  MONEY       [Chap.  VIII 

To  deny  this  conclusion  requires  a  denial  of  one 
or  more  of  the  following  premises  upon  which  it 
rests :  — 

(1)  The  equation  of  exchange,  MV  -\-  M'V  =  ^pQ. 

(2)  An  increase  of  M  normally  causes  a  proportional 
increase  of  M'. 

(3)  An  increase  of  M  does  not  normally  affect  V,  V, 
or  the  Q's. 

If  these  three  premises  be  granted,  the  conclusion 
must  be  granted.  If  any  of  the  premises  be  denied,  the 
objector  must  show  wherein  the  fallacy  lies.  Premise 
(1)  has  been  justified  in  Chapter  II  and  Chapter  III, 
and  mathematically  demonstrated  in  the  Appendices  to 
Chapters  II  and  III.  Premise  (2)  has  been  shown  to 
be  true  in  Chapter  III  and  premise  (3)  in  the  present 
chapter. 

So  much  pains  has  been  taken  to  establish  these  prem- 
ises and  to  emphasize  the  results  of  the  reasoning  based 
on  them  because  it  seems  nothing  less  than  a  scandal 
iji  Economic  Science  that  there  should  be  any  ground 
for  dispute  on  so  fundamental  a  proposition. 

The  quantity  theory  as  thus  stated  does  not  claim 
that  while  money  is  increased  in  quantity,  other  causes 
may  not  affect  M',  V,  V,  and  the  Q's,  and  thus  aggra- 
vate or  neutralize  the  effect  of  M  on  the  p's.  But  these 
are  not  the  effects  of  M  on  the  p's.  So  far  as  M  by 
itself  is  concerned,  its  effect  on  the  p's  is  strictly  propor- 
tional. 

The  importance  and  reality  of  this  proposition  are  not 
diminished  in  the  least  by  the  fact  that  these  other 
causes  do  not  historically  remain  quiescent  and  allow 
the  effect  on  the  p's  of  an  increase  in  M  to  be  seen  alone. 
The  effects  of  M  are  blended  with  the  effects  of  changes 
in  the  other  factors  in  the  equation  of  exchange  just  as 


Sec.  3]  QUANTITY  THEORY  159 

the  effects  of  gravity  upon  a  falling  body  are  blended 
with  the  effects  of  the  resistance  of  the  atmosphere. 

Finally,  it  should  be  noted  that,  in  accordance  with 
principles  previously  explained,  no  great  increase  of 
money  (M)  in  any  one  country  or  locality  can  occur 
without  spreading  to  other  countries  or  localities.  As 
soon  as  local  prices  have  risen  enough  to  make  it  profit- 
able to  sell  at  the  high  prices  in  that  place  and  buy  at 
the  low  prices  elsewhere,  money  will  be  exported.  The 
production  of  gold  in  Colorado  and  Alaska  first  results 
in  higher  prices  in  Colorado  and  Alaska,  then  in  send- 
ing gold  to  other  sections  of  the  United  States,  then  in 
higher  prices  throughout  the  United  States,  then  in 
export  abroad,  and  finally  in  higher  prices  throughout 
the  gold-using  world. 

§3 

We  have  emphasized  the  fact  that  the  strictly  pro- 
portional effect  on  prices  of  an  increase  in  M  is  only  the 
normal  or  ultimate  effect  after  transition  periods  are 
over.  The  proposition  that  prices  vary  with  money 
holds  true  only  in  comparing  two  imaginary  periods  for 
each  of  which  prices  are  stationary  or  are  moving  alike 
upward  or  downward  and  at  the  same  rate. 

As  to  the  periods  of  transition,  we  have  seen  that  an 
increase  in  M  produces  effects  not  only  on  the  p's,  but 
on  all  the  magnitudes  in  the  equation  of  exchange.  We 
saw  in  Chapter  IV  on  transition  periods  that  it  increases 
M'  not  only  in  its  normal  ratio  to  M,  but  often,  tem- 
porarily, beyond  that  ratio.  We  saw  that  it  also 
quickened  V  and  V  temporarily. 

As  previously  noted,  while  V  and  V  usually  move  in 
sympathy,  they  may  move  in  opposite  directions  when 
a  panic  decreases  confidence  in  bank  deposits.  Then 
people   pay  out   deposits  as  rapidly  as  possible  and 


160         THE    PUECHASING    POWER   OF   MONEY       [Chap.  VIII 

money  as  slowly  as  possible  —  the  last-named  tendency 
being  called  hoarding. 

We  saw  also  that  an  increase  of  M  during  a  period  of 
rising  prices  stimulated  the  Q's.     Finally  we  saw  that  a 
reduction  in  M  caused  the  reverse  effects  of  those  above 
set  forth,  decreasing  V  and  V,  decreasing  M'  not  abso- 
lutely only,  but  in  relation  to  M,  and  decreasing  the  Q's 
partly  because  of  the  disinclination  to  sell  at  low  money 
prices  which  are  believed  to  be  but  temporary,  partly 
because  of  a  slight  substitution  of  barter  for  sales;  for  if 
M  should  be  very  suddenly  reduced,  some  way  would 
have  to  be  found  to  keep  trade  going,  and  barter  would 
be  temporarily  resorted  to  in  spite  of  its  inconvenience. 
This   would   bring  some  relief,  but  its  inconvenience 
would  lead  sellers  to  demand  money  whenever  possible, 
and  prospective  buyers   to   supply  themselves   there- 
with.    The  great  pressure  to  secure  money  would  en- 
hance its  value  —  that  is,  would  lower  the  prices  of 
other  things.     This  resultant  fall  of  prices  would  make 
the  currency  more  adequate  to  do  the  business  required, 
and  make  less  barter  necessary.     The  fall  would  proceed 
until  the  abnormal  pressure,  due  to  the  inconvenience 
of   barter,   had   ceased.     Practically,    however,  in  the 
world  of  to-day,  even  such  temporary  resort  to  barter  is 
trifling.     The  convenience  of  exchange  by  money  is 
so  much  greater  than  the  convenience  of  barter,  that 
the  price  adjustment  would  be  made  almost  at  once.     If 
barter  needs  to  be  seriously  considered  as  a  relief  from 
money  stringency,  we  shall  be  doing  it  full  justice  if 
we   picture  it   as   a   safety-valve,   working   against   a 
resistance  so  great  as  almost  never  to  come  into  opera- 
tion and  then  only  for  brief  transition  intervals.     For  all 
practical  purposes  and  all  normal  cases,  we  may  assume 
that  money  and  checks  are  necessities  for  modern  trade. 


Sec.  3]  QUANTITY  THEORY  161 

The  peculiar  effects  during  transition  periods  are 
analogous  to  the  peculiar  effects  in  starting  or  stopping 
a  train  of  cars.  Normally  the  caboose  keeps  exact 
pace  with  the  locomotive,  but  when  the  train  is  starting 
or  stopping  this  relationship  is  modified  by  the  gradual 
transmission  of  effects  through  the  intervening  cars. 
Any  special  shock  to  one  car  is  similarly  transmitted 
to  all  the  others  and  to  the  locomotive. 

We  have  seen,  for  instance,  that  a  sudden  change  in 
the  quantity  of  money  and  deposits  will  temporarily 
affect  their  velocities  of  circulation  and  the  volume  of 
trade.  Reversely,  seasonal  changes  in  the  volume  of 
trade  will  affect  the  velocities  of  circulation,  and  even, 
if  the  currency  system  is  elastic,  the  quantity  of  money 
and  deposits.  In  brisk  seasons,  as  when  ''money  is 
needed  to  move  the  crops, "  the  velocity  of  circulation 
is  evidently  greater  than  in  dull  seasons.  Money  is 
kept  idle  at  one  time  to  be  used  at  another,  and  such 
seasonal  variations  in  velocity  reduce  materially  the 
variations  which  otherwise  would  be  necessary  in  the 
price  level.  In  a  similar  way  seasonal  variations  in  the 
price  level  are  reduced  by  the  alternate  expansion  and 
contraction  of  an  elastic  bank  currency.  In  this  case 
temporarily,  and  to  an  extent  limited  by  the  amount  of 
legal  tender  currency,  money  or  deposits  or  both  may 
be  said  to  adapt  themselves  to  the  amount  of  trade. 
In  these  two  ways,  then,  both  the  rise  and  fall  of  prices 
are  mitigated.^  Therefore  the  "  quantity  theory  "will 
not  hold  true  strictly  and  absolutely  during  transition 
periods. 

1  Cf.  Hildebrand,  Theorie  des  Geldes,  Chapter  XI,  who,  though 
seemingly  unconscious  of  its  bearing  on  the  velocity  of  circulation, 
calls  attention  to  the  difference  between  two  communities  having 
the  same  expenditures,  but  one  having  a  uniform  trade  and  the 
other  a  trade  "bunched"  in  certain  seasons  —  say  the  crop  seasons. 


162         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VIII 

We  have  finished  our  sketch  of  the  effects  of  M,  and 
now  proceed  to  the  other  magnitudes. 

§4 

As  to  deposits  (M'),  this  magnitude  is  always  depend- 
ent on  M.  Deposits  are  payable  on  demand  in  money. 
They  require  bank  reserves  of  money,  and  there  must 
be  some  relation  between  the  amount  of  money  in  cir- 
culation (M),  the  amount  of  reserves  (/*),  and  the 
amount  of  deposits  (M').  Normally  we  have  seen  that 
the  three  remain  in  given  ratios  to  each  other.  But 
what  is  a  normal  ratio  at  one  state  of  industry  and  civi- 
lization may  not  be  normal  at  another.  Changes  in 
population,  commerce,  habits  of  business  men,  and 
banking  facihties  and  laws  may  produce  great  changes 
in  this  ratio.  Statistically,  as  will  be  shown  in  Chapter 
XII,  the  ratio  M'/M  has  changed  from  3.1  to  4.1  in 
fourteen  years. 

Since  M'  is  normally  dependent  on  M,  we  need  not 
ask  what  are  the  effects  of  an  increase  of  Af' ;  for  these 
effects  have  been  included  under  the  effects  of  M.  But, 
since  the  ratio  of  M'  to  M  may  change,  we  do  need  to 
ask  what  are  the  effects  of  this  change. 

Suppose,  as  has  actually  been  the  case  in  recent  years, 
that  the  ratio  of  M'  to  M  increases  in  the  United  States. 
If  the  magnitudes  in  the  equations  of  exchange  in 
other  countries  with  which  the  United  States  is  con- 
nected by  trade  are  constant,  the  ultimate  effect  on  M 
is  to  make  it  less  than  what  it  would  otherwise  have 
been,  by  increasing  the  exports  of  gold  from  the  United 
States  or  reducing  the  imports.  In  no  other  way  can 
the  price  level  of  the  United  States  be  prevented  from 
rising  above  that  of  other  nations  in  which  we  have 
assumed  this  level  and  the  other  magnitudes  in  the 


JSec.  4]  QUANTITY   THEORY  163 

equation  of  exchange  to  be  quiescent.  WTiile  the  ulti- 
mate effect  then  is  to  increase  the  volume  of  circulating 
media,  this  increase  is  spread  over  the  whole  world. 
Although  the  extension  of  banking  is  purely  local,  its 
effects  are  international.  In  fact,  not  only  will  there 
be  a  redistribution  of  gold  money  over  all  gold  coun- 
tries, but  there  will  be  a  tendency  to  melt  coin  into 
bullion  for  use  in  the  arts. 

The  remaining  effects  are  the  same  as  those  of  an 
increase  in  M  which  have  already  been  studied.  That 
is,  there  will  be  no  (ultimate)  appreciable  effect  on  V, 
V,  or  the  Q's,  but  only  on  the  p's,  and  these  will  rise, 
relatively  to  what  they  would  otherwise  have  been, 
throughout  the  world.  In  foreign  countries  the  normal 
effect  will  be  proportional  to  the  increase  of  money  in 
circulation  which  they  have  acquired  through  the  dis- 
placement of  gold  in  the  United  States.  In  the  United 
States  the  effect  will  not  be  proportional  to  the  in- 
crease in  M',  since  M  has  moved  in  the  opposite  direc- 
tion. It  will  be  proportional  to  the  increase  in  M  +  M' 
if  V  and  V  are  equal,  and  less  than  in  that  proportion 
if  V  is  less  than  V,  as  is  the  actual  fact. 

In  any  case  the  effect  on  prices  is  extremely  small, 
being  spread  over  the  whole  commercial  world.  Taking 
the  world  as  a  whole,  the  ultimate  effect  is,  as  we  have 
seen,  to  raise  world  prices  slightly  and  to  melt  some 
coin.  The  only  appreciable  ultimate  effect  of  increas- 
ing the  ratio  of  M'  to  M  in  one  country  is  to  expel 
money  from  that  country  into  others.  All  of  these 
effects  are  exactly  the  same  as  those  of  increasing  the 
issue  of  bank  notes,  so  long  as  they  continue  redeem- 
able in  gold  or  other  exportable  money.  An  issue 
beyond  this  point  results  in  isolating  the  issuing  coun- 
try and  therefore  in  rapidly  raising  prices  there  in- 


164        THE    PURCHASING    POWER   OF  MONEY       [Chap.  VIII 

stead  of  spreading  the  efifect  over  other  countries. 
This  is  what  happened  in  the  United  States  during  the 
Civil  War. 

As  to  transitional  effects,  it  is  evident  that,  before 
the  expulsion  of  gold  from  the  United  States,  there  must 
be  an  appreciable  rise  in  prices  there,  of  which  traders 
will  then  take  advantage  by  selling  in  the  United  States, 
shipping  away  money,  and  buying  abroad.  During  the 
period  of  rising  prices  all  the  other  temporary  effects 
peculiar  to  such  a  period,  effects  which  have  been 
described  at  length  elsewhere,  will  be  in  evidence. 

Exactly  opposite  effects  of  course  follow  a  decrease  of 
M'  relatively  to  M. 

§5 

/We  come  next  to  the  effects  of  changes  in  velocities 
(F  and  V).  These  effects  are  closely  similar  to  those 
just  described.  The  ultimate  effects  are  on  prices,' 
and  not  on  quantity  of  money  or  volume  of  trade. 
But  a  change  in  the  velocity  of  circulation  of  money  in 
any  country,  connected  by  international  trade  with 
other  countries,  will  cause  an  opposite  change  in  the 
quantity  of  money  in  circulation  in  that  country. 
There  will  be  a  redistribution  of  money  among  the 
countries  of  the  world  and  of  money  metal  as  between 
money  and  the  arts. 

The  normal  effect,  then,  of  increasing  V  or  F'  in  any 
country  is  to  decrease  M  by  export,  to  decrease  Af' 
proportionally,  and  to  raise  prices  (p's)  slightly  through- 
out the  world.  There  is  no  reason  to  believe  that  there 
will,  normally,  be  any  effects  on  the  volume  of  trade. 
It  is  quite  possible  that  a  change  in  one  of  the  two 
velocities  will  cause  a  corresponding  change  in  the 
other,  or,  at  any  rate,  that  most  of  the  causes  which 
increase  one  will  increase  the  other.     Increased  density 


Sec.  5]  QUANTITY   THEORY  165 

of  population,  for  instance,  in  all  probability  quickens 
the  flow  both  of  money  and  checks.  Unfortunately, 
however,  we  have  not  sufficient  empirical  knowledge  of 
the  two  sorts  of  velocity  to  assert,  with  confidence,  any 
relations  between  them 

During  transition  periods  the  effects  of  changes  in 
velocities  are  doubtless  the  same  as  the  effects  of  in- 
creased currency. 

§6 

Our  next  question  is  as  to  the  effects  of  a  general 
increase  or  decrease  in  the  Q's,  i.e.  in  the  volume  of 
trade. 

An  increase  of  the  volume  of  trade  in  any  one  country, 
say  the  United  States,  ultimately  increases  the  money 
in  circulation  {M).  In  no  other  way  could  there  be 
avoided  a  depression  in  the  price  level  in  the  United 
States  as  compared  with  foreign  countries.  The  in- 
crease in  M  brings  about  a  proportionate  increase  in 
M'.  Besides  this  effect,  the  increase  in  trade  undoubt- 
edly has  some  effect  in  modifying  the  habits  of  the 
community  with  regard  to  the  proportion  of  check  and 
cash  transactions,  and  so  tends  somewhat  to  increase 
M'  relatively  to  M ;  as  a  country  grows  more  commercial 
the  need  for  the  use  of  checks  is  more  strongly  felt.^ 

As  to  effects  on  velocity  of  circulation,  we  may 
distinguish  three  cases.  The  first  is  where  the  change 
in  volume  of  trade  corresponds  to  a  change  in  popula- 

1  This  is  very  far  from  asserting  as  Laughlin  does  that  ' '  The 
limit  to  the  increase  in  legitimate  credit  operations  is  always  ex- 
pansible with  the  increase  in  the  actual  movement  of  goods" ;  see 
the  Principles  of  Money,  New  York  (Scribner),  1903,  p.  82.  We 
have  seen,  in  Chapter  IV,  that  deposit  currency  is  proportional  to 
the  amount  of  money ;  a  change  in  trade  may  indirectly,  i.e.  by 
changing  the  habits  of  the  community,  influence  the  proportion, 
but,  except  for  transition  periods,  it  cannot  influence  it  directly. 


166         THE    PURCHASING    POWER   OP   MONET       [ChAP.  VIII 

tion,  as  when  there  is  an  increase  in  trade  from  the  set- 
tUng  of  new  lands,  without  any  greater  concentration  in 
previously  settled  areas,  and  without  any  change  in  the 
per  capita  trade  or  in  the  distribution  of  trade  among 
the  elements  of  the  population.  Under  such  conditions 
no  reason  has  been  assigned,  nor  apparently  can  be  as- 
signed, to  show  why  the  velocity  of  circulation  of  money 
should  be  other  for  a  condition  in  which  the  volume  of 
trade  is  large  than  for  a  condition  in  which  it  is  small. 

The  second  case  is  where  the  increase  in  volume  of 
trade  corresponds  to  an  increased  density  of  population, 
but  no  change  in  per  capita  trade.  In  this  case,  the  closer 
settlement  may  facilitate  somewhat  greater  velocity. 

The  third  case  is  where  the  change  in  the  volume  of 
trade  does  affect  the  per  capita  trade  or  the  distribution 
of  trade  in  the  population. 

There  are  then  several  ways  in  which  the  velocity  of 
circulation  may  conceivably  be  affected.  First,  any 
change  in  trade,  implying  a  change  in  methods  of 
transportation  of  goods,  will  imply  a  change  in  meth- 
ods of  transportation  of  money ;  quick  transportation 
means  usually  more  rapid  circulation. 

Secondly,  a  changed  distribution  of  trade  will  alter 
the  relative  expenditures  of  different  persons.  If  their 
rates  of  turnover  are  different,  a  change  in  their  ex- 
penditures will  clearly  alter  the  relative  importance  or 
weighting  of  these  rates  in  the  general  average,  thus 
changing  that  average  without  necessarily  changing 
the  individual  rates  of  turnover.  For  instance,  an 
increased  trade  in  the  southern  states,  where  the  veloc- 
ity of  circulation  of  money  is  presumably  slow,  would 
tend  to  lower  the  average  velocity  in  the  United  States, 
simply  by  giving  more  weight  to  the  velocity  in  the 
slower  portions  of  the  country. 


Sec.  6]  QUANTITY   THEORY  167 

Thirdly,  a  change  in  individual  expenditures,  when 
due  to  a  real  change  in  the  quantity  of  goods  purchased, 
may  cause  a  change  in  individual  velocities.  It  seems 
to  be  a  fact  that,  at  a  given  price  level,  the  greater  a 
man's  expenditures  the  more  rapid  his  turnover;  that 
is,  the  rich  have  a  higher  rate  of  turnover  than  the 
poor.  They  spend  money  faster,  not  only  absolutely 
but  relatively  to  the  money  they  keep  on  hand.  Statis- 
tics collected  at  Yale  University  of  a  number  of  cases  of 
individual  turnover  show  this  clearly.^  In  other  words, 
the  man  who  spends  much,  though  he  needs  to  carry 
more  money  than  the  man  who  spends  little,  does  not 
need  to  carry  as  much  in  proportion  to  his  expenditure. 
This  is  what  we  should  expect ;  since,  in  general,  the 
larger  any  operation,  the  more  economically  it  can  be 
managed.  Professor  Edgeworth  ^  has  shown  that  the 
same  rule  holds  in  banking.  When  two  banks  are  con- 
solidated, the  reserve  needed  is  less  than  the  sum  of  the 
two  previous  reserves. 

We  may  therefore  infer  that,  if  a  nation  grows  richer 
per  capita,  the  velocity  of  circulation  of  money  will 
increase.  This  proposition,  of  course,  has  no  reference 
to  nominal  increase  of  expenditure.  As  we  have  seen, 
a  doubling  of  all  prices  and  incomes  would  not  affect 
anybody's  rate  of  turnover  of  money.  Each  person 
would  need  to  make  exactly  twice  the  expenditure  for 
the  same  actual  result  and  to  keep  on  hand  exactly 
twice  the  money  in  order  to  meet  the  same  contingencies 
in  the  same  way.  The  determinant  of  velocity  is  real 
expenditure,  not  nominal.  But  a  person's  real  expendi- 
ture is  only  another  name  for  his  volume  of  trade.     We 

'  See  §  1  of  Appendix  to  (this)  Chapter  VIII. 
*  "Mathematical  Theory  of  Banking,'!  Journal  of  the  Royal  Sta- 
iistical  Society,  March,  1888. 


168         THE   PURCHASING   POWER  OF  MONEY      [Chap.  VIII 

conclude,  therefore,  that  a  change  in  the  volume  of 
trade,  when  it  affects  the  per  capita  trade,  affects  ve- 
locity of  circulation  as  well. 

We  find  then  that  an  increase  in  trade,  unlike  an 
increase  in  currency  {M  and  M')  or  velocities  {V  and  V) 
has  other  effects  than  simply  on  prices  —  effects,  in 
fact,  of  increasing  magnitudes  on  the  opposite  side  of 
the  equation,  V  and  V,  and  (though  only  indirectly  by 
affecting  business  convenience  and  habit)  M'  relatively 
to  M.  If  these  effects  increase  the  left  side  as  much  as 
the  increase  in  trade  itself  (the  Q's)  directly  increases 
the  right  side,  the  effect  on  prices  will  be  nil.  If  the 
effect  on  the  left  side  exceeds  that  on  the  right,  prices 
will  rise.  Only  provided  the  effect  on  the  left  side  is 
less  than  the  increase  in  trade  will  prices  fall,  and  then 
not  proportionately  to  the  increase  in  trade. 

In  a  former  chapter,  it  was  shown  that  a  change  in 
trade,  provided  currency  {M  and  M')  and  velocities 
{V  and  V)  remained  the  same,  produced  an  inverse 
change  in  prices.  But  now  we  find  that  the  proviso  is 
inconsistent  with  the  premise ;  currency  and  velocities 
can  remain  the  same  only  by  the  clumsy  hypothesis 
that  the  various  other  causes  affecting  them  shall  be 
so  changed  as  exactly  to  neutralize  the  increase  in  trade. 
If  these  various  other  causes  remain  the  same,  then 
currency  and  velocities  will  not  remain  the  same. 

This  is  the  first  instance  in  our  study  where  we  have 
found  that  normally,  i.e.  apart  from  temporary  or 
transitional  effects,  we  reach  different  results  by  assum- 
ing causes  to  vary  one  at  a  time,  than  by  assuming  the 
algebraic  factors  in  the  equation  to  vary  one  at  a  time. 
The  ''quantity  theory"  still  holds  true  —  that  prices 
(p's)  vary  with  money  {M)  —  when  we  assume  that 
other  causes  remain  the  same,  as  well  as  when  we  assumed 


Sec.  7]  QUANTITY  THEORY  169 

merely  that  other  algebraic  factors  remain  the  same; 
and  all  the  other  theorems  stated  algebraically  were 
found  to  hold  causationally,  excepting  only  the  theorem 
as  to  variation  in  trade.  While  the  main  purpose  of 
this  chapter  is  to  justify  the  "quantity  theory"  as 
expressing  a  causal  as  well  as  an  algebraic  relation,  it  is 
important  to  point  out  that  causal  and  algebraic  theo- 
rems are  not  always  identical. 

As  to  the  transitional  effects  of  a  change  in  the 
volume  of  trade,  these  depend  mainly  on  one  of  the 
two  possible  directions  in  which  prices  move.  If 
they  move  upward,  the  transitional  effects  are  similar 
to  those  we  are  already  familiar  with  for  periods  of 
rising  prices ;  if  downward,  they  are  similar  to  those 
incident  to  such  a  movement. 


We  have  now  studied  the  effects  of  variations  in 
each  of  the  factors  in  the  equation  of  exchange  (save 
one)  on  the  other  factors.  We  have  found  that  in 
each  case  except  in  the  case  of  trade  (the  Q's)  the 
ultimate  effect  was  on  prices  (the  p's).  The  only 
group  of  factors  which  we  have  not  yet  studied  as  cause 
are  the  prices  (p's)  themselves.  Hitherto  they  have 
been  regarded  solely  as  effects  of  the  other  factors. 
But  the  objectors  to  the  quantity  theory  have  main- 
tained that  prices  should  be  regarded  as  causes  rather 
than  as  effects.  Our  next  problem,  therefore,  is  to  ex- 
amine and  criticize  this  proposition. 

So  far  as  I  can  discover,  except  to  a  limited  extent 
during  transition  periods,  or  during  a  passing  season  (e.g. 
the  fall),  there  is  no  truth  whatever  in  the  idea  that  the 
price  level  is  an  independent  cause  of  changes  in  any  of 
the  other  magnitudes  M,  M',  V,  V,  or  the  Q's.     To 


170        THE   PURCHASING   POWER   OF  MONEY       [Chap.  VIII 

show  the  untenabiHty  of  such  an  idea  let  us  grant  for 
the  sake  of  argument  that  —  in  some  other  way  than 
as  the  effect  of  changes  in  M,  M',  V,  V,  and  the  Q's  — 
the  prices  in  (say)  the  United  States  are  changed  to 
(say)  double  their  original  level,  and  let  us  see  what 
effect  this  cause  will  produce  on  the  other  magnitudes 
in  the  equation. 

It  is  clear  that  the  equality  between  the  money  side 
and  the  goods  side  must  be  maintained  somehow,  and 
that  if  the  prices  are  raised  the  quantity  of  money  or 
the  quantity  of  deposits  or  their  velocities  must  be 
raised,  or  else  the  volume  of  business  must  be  reduced. 
But  examination  will  show  that  none  of  these  solutions 
is  tenable. 

The  quantity  of  money  cannot  be  increased.  No 
money  will  come  from  abroad,  for  we  have  seen  that 
a  place  with  high  prices  drives  money  away.  The 
consequence  of  the  elevation  of  prices  in  the  United 
States  will  be  that  traders  will  sell  in  the  United  States 
where  prices  are  high,  and  take  the  proceeds  in  money 
and  buy  abroad  where  prices  are  low.  It  will  be  as 
difficult  to  make  money  flow  into  a  country  with  high 
prices  as  to  make  water  run  up  hill. 

For  similar  reasons  money  will  not  come  in  via  the 
mint.  Since  bullion  and  gold  coin  originally  had  the 
same  value  relatively  to  goods,  after  the  supposed  dou- 
bling of  prices,  gold  coin  has  lost  half  its  purchasing 
power.  No  one  will  take  bullion  to  the  mint  when  he 
thereby  loses  half  its  value.  On  the  contrary,  as  we  saw 
in  a  previous  chapter,  the  result  of  high  prices  is  to  make 
men  melt  coin. 

Finally,  the  high  prices  will  not  stimulate  mining, 
but  on  the  contrary  they  will  discourage  it,  nor  will 
high  prices  discourage  consumption  of  gold,  but  on  the 


Sec.  7]  QUANTITY  THEORY  171 

contrary  they  will  stimulate  it.  These  tendencies  have 
all  been  studied  in  detail.  Every  principle  we  have 
found  regulating  the  distribution  of  money  among 
nations  (the  distribution  of  money  metal  as  between 
money  and  the  arts  or  the  production  and  consumption 
of  metals)  works  exactly  opposite  to  what  would  be 
necessary  in  order  to  bring  money  to  fit  prices  instead 
of  prices  to  fit  money. 

It  is  equally  absurd  to  expect  high  prices  to  increase 
the  quantity  of  deposits  (M').  We  have  seen  that 
the  effect  would  be  to  diminish  the  quantity  of  money 
in  circulation  (M) ;  but  this  money  is  the  basis  of  the 
deposit  currency  {M'),  and  the  shrinkage  of  the  first 
will  entail  the  shrinkage  of  the  second.  The  reduction 
of  M  and  M'  will  not  tend  to  favor,  but  on  the  con- 
trary will  tend  to  pull  down  the  high  prices  we  have 
arbitrarily  assumed. 

The  appeal  to  the  velocities  (F  and  F')  is  no  more 
satisfactory.  These  have  already  been  adjusted  to 
suit  individual  convenience.  To  double  them  might 
not  be  a  physical  possibility,  and  would  certainly  be 
a  great  inconvenience. 

There  is  left  the  forlorn  hope  that  the  high  prices  will 
diminish  trade  (the  Q's).  But  if  all  prices  including 
the  prices  of  services  are  doubled,  there  is  no  reason 
why  trade  should  be  reduced.  Since  the  average  person 
will  not  only  pay,  but  also  receive  high  prices,  it  is 
evident  that  the  high  prices  he  gets  will  exactly  make 
him  able  to  stand  the  high  prices  he  pays  without 
having  to  reduce  his  purchases. 

We  conclude  that  the  hjrpothesis  of  a  doubled  price 
level  acting  as  an  independent  cause  controlling  the 
other  factors  in  the  equation  of  exchange  and  uncon- 
trolled by  them  is  untenable.   Any  attempt  to  maintain 


172        THE    PURCHASING   POWER   OF   MONEY       [Chap.  VIII 

artificially  high  prices  must  result,  as  we  have  seen,  not 
in  adjusting  the  other  elements  in  the  equation  of  ex- 
change to  suit  these  high  prices,  but  on  the  contrary 
in  arousing  their  antagonism.  Gold  will  go  abroad 
and  into  the  melting  pot,  will  be  produced  less  and 
consumed  more  until  its  scarcity  as  money  will  pull 
down  the  prices.  The  price  level  is  normally  the  one 
absolutely  passive  element  in  the  equation  of  exchange. 
It  is  controlled  solely  by  the  other  elements  and  the 
causes  antecedent  to  them,  but  exerts  no  control  over 
them. 

But  though  it  is  a  fallacy  to  think  that  the  price  level 
in  any  community  can,  in  the  long  run,  affect  the 
money  in  that  community,  it  is  true  that  the  price  level 
in  one  community  may  affect  the  money  in  another 
community.  This  proposition  has  been  repeatedly 
made  use  of  in  our  discussion,  and  should  be  clearly 
distinguished  from  the  fallacy  above  mentioned.  The 
price  level  in  an  outside  community  is  an  influence 
outside  the  equation  of  exchange  of  that  community, 
and  operates  by  affecting  its  money  in  circulation  and 
not  by  directly  affecting  its  price  level.  The  price  level 
outside  of  New  York  City,  for  instance,  affects  the 
price  level  in  New  York  City  only  via  changes  in  the 
money  in  New  York  City.  Within  New  York  City 
it  is  the  money  which  influences  the  price  level,  and  not 
the  price  level  which  influences  the  money.  The  price 
level  is  effect  and  not  cause.  Moreover,  although  the 
price  level  outside  of  New  York  is  a  proximate  cause 
of  changes  of  money  in  New  York,  that  price  level  in 
turn  is  cause  only  in  a  secondary  sense,  being  itself  an 
effect  of  the  other  factors  in  the  equation  of  exchange 
outside  of  New  York  City.  For  the  world  as  a  whole 
the  price  level  is  not  even  a  secondary  cause,  but  solely 


Sec    7]  QUANTITY  THEORY  173 

an  effect  —  of  the  world's  money,  deposits,  velocities^ 
and  trade. 

We  have  seen  that  high  prices  in  any  place  do  not 
cause  an  increase  of  the  money  supply  there;  for  money 
flows  away  from  such  a  place.  In  the  same  way  high 
prices  at  any  time  do  not  cause  an  increase  of  money 
at  that  time;  for  money,  so  to  speak,  flows  away  from 
that  time.  Thus  if  the  price  level  is  high  in  January  as 
compared  with  the  rest  of  the  year,  bank  notes  will  not 
tend  to  be  issued  in  large  quantities  then.  On  the  con- 
trary, people  will  seek  to  avoid  paying  money  at  the 
high  prices  and  wait  till  prices  are  lower.  When  that 
time  comes  they  may  need  more  currency;  bank  notes 
and  deposits  may  then  expand  to  meet  the  excessive 
demands  for  loans  which  may  ensue.  Thus  currency 
expands  when  prices  are  low  and  contracts  when  prices 
are  high,  and  such  expansion  and  contraction  tend  to 
lower  the  high  prices  and  raise  the  low  prices,  thus  work- 
ing toward  mutual  equality.  We  see  then  that,  so  far  from 
its  being  true  that  high  prices  cause  increased  supply  of 
money,  it  is  true  that  money  avoids  the  place  and  time 
of  high  prices  and  seeks  the  place  and  time  of  low 
prices,  thereby  mitigating  the  inequality  of  price  levels. 

What  has  been  said  presupposes  that  purchasers  have 
the  option  to  change  the  place  and  time  of  their  pur- 
chases. To  the  extent  that  their  freedom  to  choose 
their  market  place  or  time  is  interfered  with,  the  cor- 
rective adjustment  of  the  quantity  of  money  is  pre- 
vented. The  anomalous  time  of  a  panic  may  even  be 
characterized  by  necessity  to  meet  old  contracts  which 
afford  no  choice  of  deferring  the  payment.  There  may 
then  be  a  "money  famine"  and  a  feverish  demand  for 
emergency  currency  needed  to  liquidate  outstanding 
contracts  which  would  never  have  been  entered  into  if 


174        THE    PURCHASING   POWER   OF  MONEY       [Chap.  VIII 

the  situation  had  been  foreseen.  That  such  anomalous 
conditions  do  not  negative  the  general  thesis  that  prices 
are  the  effect  and  not  the  cause  of  currency  (including 
deposit  currency)  is  shown  statistically  by  Minnie 
Throop  England.^ 

§8 

Were  it  not  for  the  fanatical  refusal  of  some  econo- 
mists to  admit  that  the  price  level  is  in  ultimate  anal- 
ysis effect  and  not  cause,  we  should  not  be  at  so  great 
pains  to  prove  it  beyond  cavil.  It  is  due  our  science 
to  demonstrate  its  truths.  The  obligation  to  do  this 
carries  with  it  the  obligation  to  explain  if  possible  why 
so  obvious  a  truth  has  not  been  fully  accepted. 

One  reason  has  already  been  cited,  the  fear  to  give 
aid  and  comfort  to  the  enemies  of  all  sound  economists, 
—  the  unsound  money  men.  Another  may  now 
receive  attention,  viz.  the  fallacious  idea  that  the 
price  level  cannot  be  determined  by  other  factors  in 
the  equation  of  exchange  because  it  is  already  deter- 
mined by  other  causes,  usually  alluded  to  as  ''supply 
and  demand,"  This  vague  phrase  has  covered  multi- 
tudes of  sins  of  slothful  analysts  in  economics.  Those 
who  place  such  implicit  reliance  on  the  competency  of 
supply  and  demand  to  fix  prices,  irrespective  of  the 
quantity  of  money,  deposits,  velocity,  and  trade,  will 
have  their  confidence  rudely  shaken  if  they  will  follow 
the  reasoning  as  to  price  causation  of  separate  articles. 
They  will  find  that  there  are  always  just  one  too  few 
equations  to  determine  the  unknown  quantities  in- 
volved.2    The  equation  of  exchange  is  needed  in  each 

^  "  Statistical  inquiry  into  the  influence  of  credit  upon  the  level 
of  prices,"  University  Studies  (University  of  Nebraska),  January, 
1907,  pp.  41-83. 

*  Cf.  Irving  Fisher,  "  Mathematical  Investigations  in  the  Theory 


Sec.  8J  QUANTITY  THEORY  175 

case  to  supplement  the  equations  of  supply  and 
demand. 

It  would  take  us  too  far  afield  to  insert  here  a  com- 
plete statement  of  price-determining  principles.  But 
the  compatibility  of  the  equation  of  exchange  with 
the  equations  which  have  to  deal  with  prices  individu- 
ally may  be  brought  home  to  the  reader  sufficiently  for 
our  present  purposes  by  emphasizing  the  distinction 
between  (1)  individual  prices  relatively  to  each  other 
and  (2)  the  price  level.  The  equation  of  exchange  de- 
termines the  latter  (the  price  level)  only,  and  the  latter 
only  is  the  subject  of  this  book.  It  will  not  help,  but 
only  hinder  the  reader  to  mix  with  the  discussion  of 
price  levels  the  principles  determining  individual  prices 
relatively  to  each  other.  It  is  amazing  how  tenaciously 
many  people  cling  to  the  mistaken  idea  that  an  indi- 
vidual price,  though  expressed  in  money,  may  be  deter- 
mined wholly  without  reference  to  money.  Others, 
more  open-minded  but  almost  equally  confused,  see  the 
necessity  of  including  the  quantity  of  money  among  the 
causes  determining  prices,  but  in  the  careless  spirit  of 
eclecticism  simply  jumble  it  in  with  a  miscellaneous 
collection  of  influences  affecting  prices,  with  no  regard 
for  their  mutual  relations.  It  should  be  clearly  recog- 
nized that  price  levels  must  be  studied  independently  of 
individual  prices. 

The  legitimacy  of  separating  the  study  of  price  levels 
from  that  of  prices  will  be  clearly  recognized,  when  it  is 
seen  that  individual  prices  cannot  be  fully  determined 
by  supply  and  demand,  money  cost  of  production,  etc., 
without  surreptitiously  introducing  the  price  level 
itself.     We  can  scarcely  overemphasize  the  fact  that 

and  Value  of  Prices,"  Transactions  of  the  Connecticut  Academy  of 
Arts  and  Sciences,  Vol.  IX,  1892,  p.  62. 


176         THE    PURCHASING   POWER   OF   MONEY       [Chap.  VIII 

the  ''supply  and  demand"  or  the  ''cost  of  production" 
of  goods  in  terms  of  money  do  not  and  cannot  com- 
pletely determine  prices.  Each  phrase,  fully  expressed, 
already  implies  mo7iey.  There  is  always  hidden  some- 
where the  assumption  of  a  general  price  level.  Yet 
writers,  like  David  A.  Wells,  ^  have  seriously  sought 
the  explanation  of  a  general  change  in  price  levels  in  the 
individual  price  changes  of  various  commodities  con- 
sidered separately.  Much  of  their  reasoning  goes  no 
farther  than  to  explain  one  price  in  terms  of  other 
prices.  If  we  attempt  to  explain  the  money  price  of 
a  finished  product  in  terms  of  the  money  prices  of  its 
raw  materials  and  other  money  costs  of  prices  of  pro- 
duction, it  is  clear  that  we  merely  shift  the  problem. 
We  have  still  to  explain  these  antecedent  prices.  In 
elementary  textbooks  much  emphasis  is  laid  on  the 
fact  that  "demand"  and  "supply"  are  incomplete 
designations  and  that  to  give  them  meaning  it  is  neces- 
sary to  add  to  each  the  phrase  "at  a  price."  But 
emphasis  also  needs  to  be  laid  on  the  fact  that  "demand 
at  a  price"  and  "supply  at  a  price"  are  still  incom- 
plete designations,  and  that  to  give  them  meaning  it 
is  necessary  to  add  "at  a  price  level."  The  demand 
for  sugar  is  not  only  relative  to  the  price  of  sugar,  but 
also  to  the  general  level  of  other  things.  Not  only 
is  the  demand  for  sugar  at  ten  cents  a  pound  greater 
than  the  demand  at  twenty  cents  a  pound  (at  a  given 
level  of  prices  of  other  things),  but  the  demand  at 
twenty  cents  at  a  high  level  of  prices  is  greater  than  the 
demand  at  twenty  cents  at  a  low  level  of  prices.  In 
fact  if  the  price  level  is  doubled,  the  demand  at  twenty 
cents  a  pound  will  be  as  great  as  the  demand  was  before 

'  Recent  Economic  Changes,  New  York  (Appleton),  1890,  Chap- 
ter IV. 


Sec.  8]  QUANTITY  THEORY  177 

at  ten  cents  a  pound,  assuming  that  the  doubling  apphes 
likewise  to  wages  and  incomes  generally.  The  signifi- 
cance of  a  dollar  lies  in  what  it  will  buy ;  and  the  equiv- 
alence between  sugar  and  dollars  is  at  bottom  an  equiv- 
alence between  sugar  and  what  dollars  will  buy.  A 
change  in  the  amount  of  what  dollars  will  buy  is  as 
important  as  a  change  in  the  amount  of  sugar.  The 
price  of  sugar  in  dollars  depends  partly  on  sugar  and 
partly  on  dollars,  —  that  is,  on  what  dollars  will  buy 
—  that  is,  on  the  price  level.  Therefore,  beneath  the 
price  of  sugar  in  particular  there  lies,  as  one  of  the  bases 
of  that  particular  price,  the  general  level  of  prices.  We 
have  more  need  to  study  the  price  level  preparatory 
to  a  study  of  the  price  of  sugar  than  to  study  the  price 
of  sugar  preparatory  to  a  study  of  the  price  level. 
We  cannot  explain  the  level  of  the  sea  by  the  height 
of  its  individual  waves;  rather  must  we  explain  in 
part  the  position  of  these  waves  by  the  general  level 
of  the  sea.  Each  ''supply  curve"  or  "demand  curve" 
rests  upon  the  unconscious  assumption  of  a  price  level 
already  existing.  Although  the  curves  relate  to  a  com- 
modity, they  relate  to  it  only  as  compared  with  money. 
A  price  is  a  ratio  of  exchange  between  the  commodity 
and  money.  The  money  side  of  each  exchange  must 
never  be  forgotten  nor  the  fact  that  money  already 
stands  in  the  mind  of  the  purchaser  for  a  general  pur- 
chasing power.  Although  every  buyer  and  seller  who 
bids  or  offers  a  price  for  a  particular  commodity  tacitly 
assumes  a  given  purchasing  power  of  the  money  bid  or 
offered,  he  is  usually  as  unconscious  of  so  doing  as  the 
spectator  of  a  picture  is  unconscious  of  the  fact  that  he 
is  using  the  background  of  the  picture  against  which  to 
measure  the  figures  in  the  foreground.  As  a  conse- 
quence, if  the  general  level  changes,  the  supply  and 


178         THE    PURCHASING    POWER   OF   MONEY       [Chap.  Vlii 

demand  curves  for  the  particular  commodity  considered 
will  change  accordingly.  If  the  purchasing  power  of 
the  dollar  is  reduced  to  half  its  former  amount,  these 
curves  will  be  doubled  in  height ;  for  each  person  will 
give  or  take  double  the  former  money  for  a  given 
quantity  of  the  commodity.  If,  through  special  causes 
affecting  a  special  commodity,  the  supply  and  demand 
curves  of  that  commodity  and  their  intersection  are 
raised  or  lowered,  then  the  supply  and  demand  curves 
of  some  other  goods  must  change  in  the  reverse  direc- 
tion. That  is,  if  one  commodity  rises  in  price  (without 
any  change  in  the  quantity  of  it  or  of  other  things 
bought  and  sold,  and  without  any  change  in  the  volume 
of  circulating  medium  or  in  the  velocity  of  circulation), 
then  other  commodities  must  fall  in  price.  The  in- 
creased money  expended  for  this  commodity  will  be 
taken  from  other  purchases.  In  other  words,  the  waves 
in  the  sea  of  prices  have  troughs.  This  can  be  seen  from 
the  equation  of  exchange.  If  we  suppose  the  quantity 
of  money  and  its  velocity  of  circulation  to  remain 
unaltered,  the  left  side  of  the  equation  remains  the 
same,  and  therefore  the  right  side  must  remain  unal- 
tered also.  Consequently,  any  increase  in  one  of  its 
many  terms,  due  to  an  increase  of  any  individual  price, 
must  occur  at  the  expense  of  the  remaining  terms. 

It  is,  of  course,  true  that  a  decrease  in  the  price  of  any 
particular  commodity  will  usually  be  accompanied 
by  an  increase  in  the  amount  of  it  exchanged,  so  that 
the  product  of  the  two  may  not  decrease  and  may  even 
increase  if  the  amount  exchanged  increases  sufficiently. 
In  this  case,  since  the  right  side  of  our  equation  re- 
mains the  same,  the  effect  of  the  increase  in  some 
terms  will  necessarily  be  a  decrease  in  others ;  and  the 
remaining  terms  of  the  right  side  must  decrease  to  some 


Sec.  8]  QUANTITY   THEORY  179 

extent.  The  effect  may  be  a  general  or  even  a  universal 
lowering  of  prices.  Even  in  this  case  the  reduction  in 
the  price  level  has  no  direct  connection  with  the  reduc- 
tion in  the  price  of  the  particular  commodity,  but  is 
due  to  the  increase  in  the  amount  of  it  exchanged.^ 

The  reactionary  effect  of  the  price  of  one  commodity 
on  the  prices  of  other  conunodities  must  never  be  lost 
sight  of.  Much  confusion  will  be  escaped  if  we  give 
up  any  attempt  to  reason  directly  from  individual 
prices.  Improvements  in  production  will  affect  price 
levels  simply  as  they  affect  the  volume  of  business 
transacted.  Any  rational  study  of  the  influence  of 
improvements  in  methods  of  production  upon  the  level 
of  prices  should,  therefore,  fix  attention,  first,  on  the 
resulting  volume  of  trade,  and  should  aim  to  discover 
whether  this,  in  turn,  carries  prices  upwards  or  down- 
wards. 

One  of  the  supposed  causes  of  high  prices  to-day, 
much  under  discussion  at  the  present  time,  is  that  of 
industrial  and  labor  combinations.  From  what  has 
been  said,  it  must  be  evident  that,  other  things  remain- 
ing equal,  trusts  cannot  affect  the  general  level  of  prices 
through  manipulating  special  commodities  except  as 
they  change  the  amounts  sold.  If  prices  for  one  com- 
modity are  changed  without  a  change  in  the  number 
of  sales,  the  effect  on  the  price  level  will  be  neutralized 
by  compensatory  changes  in  other  prices.  If  trade 
unions  seek  to  raise  prices  of  labor  while  trusts  raise 
prices  of  commodities,  the  general  level  of  everything 
may  rise  or  fall;  but  it  can  rise  only  by  a  general 
decrease  in  the  quantities  of  commodities,  labor,  etc., 
sold,  or  by  an  increase  of  currency,  or  by  an  increase  in 
velocities  of  circulation.  If  there  is  neither  an  increase 
*  For  further  discussion,  see  §  2  of  Appendix  to  (this)  Chapter  VIII. 


180         THE    PURCHASING    POWER   OF   MONEY       [Chap.  VIII 

nor  decrease  in  volume  of  business,  and  if  the  quantity 
and  velocity  of  circulation  of  money  and  its  substitutes 
remain  unchanged,  the  price  level  cannot  change. 
Changes  in  some  parts  of  the  price  level  may  occur  only 
at  the  expense  of  opposite  changes  in  other  parts. 

We  have  seen  that  the  price  level  is  not  determined 
by  individual  prices,  but  that,  on  the  contrary,  any 
individual  price  presupposes  a  price  level.  We  have 
seen  that  the  complete  and  only  explanation  of  a  price 
level  is  to  be  sought  in  factors  of  the  equation  of  ex- 
change and  whatever  antecedent  causes  affect  those 
factors.  The  terms  ''demand"  and ''supply, "  used  in 
reference  to  particular  prices,  have  no  significance  what- 
ever in  explaining  a  rise  or  fall  of  price  levels.  In  con- 
sidering the  influence  affecting  individual  prices  we  say 
that  an  increase  in  supply  lowers  prices,  but  an  increase 
in  demand  raises  them.  But  in  considering  the  influ- 
ences affecting  price  levels  we  enter  upon  an  entirely 
different  set  of  concepts,  and  must  not  confuse  the  prop- 
osition that  an  increase  in  the  trade  (the  Q's)  tends  to 
lower  the  price  level,  with  the  proposition  that  an  in- 
crease in  supply  tends  to  lower  an  individual  price. 
Trade  (the  Q's)  is  not  supply  —  in  fact  is  no  more  to 
be  associated  with  supply  than  with  demand.  The  Q's 
are  the  quantities  finally  sold  by  those  who  supply,  and 
bought  by  those  who  demand. 

We  may  here  state  a  paradox  which  will  serve  to 
bring  out  clearly  the  distinction  between  the  causation 
of  individual  prices  relatively  to  each  other  and  the 
causation  of  the  general  level  of  prices.  The  paradox 
is  that  although  an  increased  demand  for  any  individual 
commodity  results  in  a  greater  consumption  at  a  higher 
price,  yet  an  increased  general  demand  for  goods  will 
result  in  a  greater  trade  (the  Q's)  at  lower  prices. 


Bec.  9]  QUANTITY   THEORY  181 

We  cannot,  therefore,  reason  directly  from  particular 
to  general  prices;  we  can  reason  only  indirectly  by  refer- 
ence to  the  effects  on  quantities.  Sometimes  the  rise 
in  an  individual  price  raises  and  at  other  times  lowers 
the  general  price  level.  ^  To  draw  a  physical  parallel 
let  us  suppose  that  a  thousand  piles  have  been  driven 
in  a  quicksand  and  that  the  owner  wishes  to  raise  their 
level  a  foot.  He  gets  hoisting  apparatus  and  planting 
it  on  the  piles  pulls  one  of  them  up  a  foot.  He  then 
pulls  up  another  and  continues  until  he  has  pulled  up 
each  of  the  thousand.  But  if  every  time  he  has  pulled 
one  up  a  foot  he  has  pushed  down  999  over  g^g  of  a 
foot,  when  he  has  finished,  he  will  find  his  thousand 
piles  lower  than  when  he  began.  Each  time  a  pile  has 
risen,  the  average  level  of  all  has  fallen. 

The  proposition  that  a  general  increase  in  demand, 
resulting  in  an  increase  in  trade,  tends  to  decrease  and 
and  not  to  increase  the  general  level  of  prices,  may  be 
regarded  as  a  sort  of  pons  asinorum  to  test  one's  knowl- 
edge of  the  fundamental  distinction  between  those 
influences  affecting  the  general  price  level  and  those 
affecting  the  rise  and  fall  of  a  particular  price  with  re- 
spect to  that  level. 

§  9 

We  have  seen  that  the  various  factors  represented  in 
the  equation  of  exchange  do  not  stand  on  the  same 
causal  footing.  Prices  are  the  passive  element  and  their 
general  level  must  conform  to  the  other  factors.  The 
causal  propositions  we  have  found  to  be  true  normally, 
i.e.  after  transitions  are  completed,  are  in  brief  as 
follows :  — 

1.  An  increase  in  the  quantity  of  money  (M)  tends 

'  For  further  discussion,  see  §  2  of  Appendix  to  (this)  Chapter 
VIII. 


182         THE    PURCHASING   POWER   OF  MONEY       [Chap.  VIIX 

to  increase  deposits  (M')  proportionally,  and  the  increase 
in  these  two  (M  and  M')  tends  to  increase  prices  pro- 
portionally. 

2.  An  increase  in  the  quantity  of  money  in  one 
country  tends  to  spread  to  others  using  the  same  money 
metal,  and  to  the  arts,  as  soon  as  the  price  levels  or  the 
relative  value  of  money  and  bullion  differ  enough  to 
make  export  or  melting  of  the  money  metal  profitable 
and  to  raise  slightly  world  prices. 

3.  An  increase  in  deposits  (M')  compared  with  money 
(M)  tends  likewise  to  displace  and  melt  coin,  and  to 
raise  world  prices. 

4.  An  increase  in  velocities  tends  to  produce  similar 
effects. 

5.  An  increase  in  the  volume  of  trade  (the  Q's)  tends, 
not  only  to  decrease  prices,  but  also  to  increase  velocities 
and  deposits  relatively  to  money  and  through  them  to 
neutralize  partly  or  wholly  the  said  decrease  in  prices. 

6.  The  price  level  is  the  effect  and  cannot  be  the  cause 
of  change  in  the  other  factors. 

7.  Innumerable  causes  outside  the  equation  of  ex- 
change may  affect  M,  M' ,  V,  V ,  and  the  Q'sand  through 
them  affect  the  p's.  Among  these  outside  causes  are 
the  price  levels  in  surrounding  countries. 

8.  The  causation  of  individual  prices  can  only  explain 
prices  as  compared  among  themselves.  It  cannot  ex- 
plain the  general  level  of  prices  as  compared  with  money. 

9.  Some  of  the  foregoing  propositions  are  subject 
to  slight  modification  during  transition  periods.  It  is 
then  true,  for  instance,  that  an  increase  in  the  quantity 
of  money  {M)  besides  having  the  effects  above  men- 
tioned will  change  temporarily  the  ratio  of  M'  to  M  and 
disturb  temporarily  V,  V,  and  the  Q's,  making  a  credit 
cycle. 


Sec.  9]  QUANTITY  THEORY  183 

In  general,  then,  our  conclusion  as  to  causes  and 
effects  is  that  normally  the  price  level  (the  p's)  is  the 
effect  of  all  the  other  factors  in  the  equation  of  exchange 
(M,  M',  V,  F',  and  the  Q's) ;  that  among  these  other 
factors,  deposits  {M')  are  chiefly  the  effect  of  money, 
given  the  normal  ratio  of  M'  to  M ;  that  this  ratio  is 
partly  the  effect  of  trade  ( the  Q's) ;  that  V  and  V  are 
also  partly  the  effects  of  the  Q's ;  and  that  all  of  the 
magnitudes,  M,  M',  V,  V,  and  the  Q's  are  the  effects  of 
antecedent  causes  outside  the  equation  of  exchange,  ad 
infinitum. 

The  main  conclusion  is  that  we  find  nothing  to  inter- 
fere with  the  truth  of  the  quantity  theory  that  variations 
in  money  (M)  produce  normally  proportional  changes 
in  prices. 


CHAPTER  IX 

THE   DISPERSION   OF   PRICES   MAKES   NECESSARY   AN 
INDEX   OF   PURCHASING   POWER 

§    1 

We  have  found  that  the  general  level  of  prices  is 
determined  by  the  other  magnitudes  in  the  equation,  of 
exchange.  But  we  have  not  hitherto  defined  exactly 
what  a  "general  level"  may  mean.  There  was  no  need 
of  such  a  definition  so  long  as  we  assumed,  as  we  have 
usually  done  hitherto,  that  all  prices  move  in  perfect 
unison.  But  practically  prices  never  do  move  in  per- 
fect unison.  Their  dispersion  would  render  impossible 
the  statistical  study  of  general  price  movements  were 
there  no  practical  method  of  indicating  the  general 
movement.  A  simple  figure  indicating  the  general 
trend  of  thousands  of  prices  is  a  great  statistical  con- 
venience. It  also  simplifies  our  equation  of  exchange 
by  converting  the  right  side,  which  now  consists  of 
thousands  of  terms,  into  a  single  simple  term. 

Such  an  indication  is  called  an  "index  number"  of 
the  price  level.  Its  reciprocal  indicates,  of  course,  the 
purchasing  power  of  money. 

The  present  chapter  will,  then,  treat  of  the  dispersion 
of  prices,  the  next  chapter  of  index  numbers  which  this 
dispersion  renders  a  practical  necessity,  and  the  two 
following  chapters  of  the  practical  statistical  use  of  index 
numbers. 

The  chief  conclusion  of  our  previous  study  is  that  an 
increase  of  money,  other  things  equal,  causes  a  pro- 

184 


Sec.  1]  DISPERSION    OF   PRICES  185 

portional  increase  in  the  level  of  prices.  In  other  words, 
the  p's  in  the  sum  SpQ  tend  to  rise  in  proportion 
to  the  increase  in  money.  It  was  noted,  however,  that 
the  adjustment  is  not  necessarily  uniform,  and  that 
if  some  p's  do  not  rise  as  much  as  in  this  proportion, 
others  must  rise  more.  In  this  connection,  we  observe 
that  some  prices  cannot  adjust  themselves  at  once, 
and  some  not  at  all.  This  latter  is  true,  for  instance, 
of  prices  fixed  by  contract.  A  price  so  fixed  cannot 
be  affected  by  any  change  coming  into  operation  be- 
tween the  date  of  the  contract  and  that  of  its  fulfillment. 
Even  in  the  absence  of  explicit  contracts,  prices  may  be 
kept  from  adjustment  by  implied  understandings  and 
by  the  mere  inertia  of  custom.  Besides  these  restric- 
tions on  the  free  movement  of  prices,  there  are  often 
legal  restrictions ;  as,  for  example,  when  railroads  are 
prohibited  from  charging  over  two  cents  per  passenger 
per  mile,  or  when  street  railways  are  limited  to  five-cent 
or  three-cent  fares. 

Whatever  the  causes  of  nonadjustment,  the  result  is 
that  the  prices  which  do  change  will  have  to  change  in 
a  greater  ratio  than  would  be  the  case  were  there  no 
prices  which  do  not  change.  Just  as  an  obstruction 
put  across  one  half  of  a  stream  causes  an  increase  in 
current  in  the  other  half,  so  any  deficiency  in  the  move- 
ment of  some  prices  must  cause  an  excess  in  the  move- 
ment of  others. 

In  order  to  picture  to  ourselves  what  are  the  classes 
of  prices  which  rise  or  fall,  we  must  survey  the  entire 
field  of  prices.  Prices,  measured  as  we  are  accustomed 
to  measure  them,  in  terms  of  money,  are  the  ratios  of 
exchange  between  other  goods  and  money.  The 
term  "goods,"  as  previously  explained,  is  a  collective 
term   comprising   all   wealth,    property,  and   services, 


186  THE   PURCHASING   POWER  OF  MONEY         [Chap.  IX 

these  being  the  magnitudes  designated  in  sales.  The 
chief  subclasses  under  these  three  groups,  which  occur 
in  actual  sales,  may  be  indicated  as  follows :  — 


Wealth 


Property 


Services 


j  Real  estate 
[  Commodities 

Stocks 

Bonds 

Mortgages 

Private  notes 

Time  bills  of  exchange 

Of  rented  real  estate 

Of  rented  commodities 

Of  hired  workers 
.  Of  some  or  all  these  agencies  combined. 


The  prices  of  these  various  classes  of  goods  cannot 
all  move  up  and  down  in  perfect  unison.  Some  are  far 
more  easily  adjustable  than  others.  Only  by  extremely 
violent  hypotheses  could  we  imagine  perfect  adjust- 
ability in  all.  The  order  of  adjustability  from  the  least 
to  the  most  adjustable  may  be  roughly  indicated  as 
follows :  ^  — 

1.  Contract  prices  of  properties  and  services,  espe- 
cially where  the  contracts  are  for  a  long  time ;  these  in- 
clude bonds,  mortgage  notes,  use  of  real  estate  by  leases. 

2.  Contract  prices  of  properties  and  services,  where 
the  contracts  are  for  a  shorter  time ;  these  include 
bills  of  exchange,  use  of  rented  real  estate  and  com- 
modities, services  of  workmen,  etc. 

1  Cf.  Jevons's  admirable  "  Classification  of  Incomes  according  as 
they  suffer  from  Depreciation,"  Investigations  in  Currency  and 
Finance,  London  (Macmillan),  1884,  p.  80,  and  after.  See  also  The 
Gold  Siipply  and  Prosperity,  edited  by  Byron  W.  Holt,  New  York 
(The  Moody  Corporation),  1907,  especially  the  Conclusion  or 
Summary  by  the  editor,  beginning  on  page  193. 


Sec.  1]  DISPERSION   OF   PRICES  187 

3.  Prices  of  commodities  made  of  the  money  metal. 

4.  Prices  of  substitutes  for  said  commodities. 

5.  Prices  fixed  by  law,  as  court  fees,  postage,  tolls, 
use  of  public  utilities,  salaries,  etc. 

6.  Prices  fixed  by  custom,  as  medical  fees,  teachers' 
salaries,  etc.,  and  to  some  extent  wages. 

7.  Prices  of  real  estate. 

8.  Prices  of  most  commodities  at  retail. 

9.  Prices  of  most  commodities  at  wholesale. 
10.  Prices  of  stocks. 

Take,  for  instance,  bonds  and  mortgages.  In  order 
that  the  prices  of  these  may  be  perfectly  adjustable,  we 
should  have  to  suppose,  not  only  that  there  were  no 
restraint  from  custom  or  law,  but  that  the  contracts 
were  perfectly  readjusted  to  each  new  price  level. 
We  should  have  to  suppose,  for  instance,  that  after 
the  price  level  had  doubled  in  height,  because  cur- 
rency had  doubled,  there  would  be  a  $2000  bond 
wherever  there  had  been  a  $1000  bond.  This,  obvi- 
ously, is  not  the  case.  The  holder  of  a  $1000  bond 
can  receive  at  its  maturity  only  $1000,  besides  in- 
terest payments  in  the  interim.  If,  meanwhile,  the 
price  level  doubles,  he  will  receive  no  more.  It  is 
true  that  a  change  of  price  level  will,  in  time,  change 
the  volume  of  new  loans.  A  merchant,  to  lay  in  a 
given  stock  of  goods,  will  need  to  borrow  a  larger 
sum  if  prices  are  high  than  if  they  are  low.  Per- 
sonal notes  and  bills  of  exchange  will  be  drawn  for 
double  the  amount  which  would  have  obtained  had 
the  price  level  not  doubled.  Similarly,  a  corporation 
issuing  bonds  for  new  projects  may  have  to  issue  a 
larger  amount.  But  obligations  outstanding  when  the 
price  levels  change  cannot  be  thus  adjusted;  their 
prices  can  vary  only  slightly  during  the  interim  be- 


188  THE    PURCHASING   POWER   OF   MONEY         (Chap.  IX 

tween  issue  and  maturity.  The  fact  that  their  face 
value  is  expressed  in  money  sets  very  definite  Umits 
to  their  prices.^  If,  because  of  a  doubling  in  the  quan- 
tity of  money,  the  value  and  profits  of  a  railroad 
measured  in  money  were  doubled,  the  bondholder  could 
not,  on  that  account,  realize  more  money  for  his  bond. 
The  value  of  the  bond  is  not  greatly  affected  by  the 
valuation  and  profits  of  the  railroad,  so  long  as  these 
are  sufficient  to  guarantee  the  bond.  The  bond  is  an 
agreement  to  pay  stated  sums  at  stated  times.  It  repre- 
sents a  limited  money  value  carved  out  of  the  road. 
The  only  ways  in  which  the  money  price  of  a  bond  or 
salable  debt  can  vary  at  all  are  by  variations  in  the 
rate  of  money  interest  and  by  changes  in  the  degree  of 
certainty  of  payment.  Only  so  far  as  these  features  are 
affected  by  the  changes  in  the  volume  of  money  will 
the  value  of  bonds  be  affected.  We  have  seen,  for  in- 
stance, that  inflation,  while  it  is  taking  place,  raises 
interest.^  It  therefore  lowers  the  price  of  bonds  during 
the  transition  period.^  Again  if  violent  changes  in  the 
price  level  increase  or  decrease  the  number  of  bank- 
ruptcies, they  thereby  affect  the  degree  of  certainty  of 
payment,  and  consequently  affect  the  value  of  bonds. 
But  these  ways  of  affecting  prices  of  such  securities  ex- 
pressed in  money  are  of  less  account  than  the  ordinary 
effect  of  inflation  or  contraction  on  price  levels,  and  of 
a  different  character. 

1  See  article  by  Walter  S.  Logan  on  the  "Duty  of  Gold,"  in  The 
Gold  Supply  and  Prosperity,  edited  by  Byron  W.  Holt,  New  York 
(The  Moody  Corporation),  1907,  p.  106.  See  also  Ricardo,  "Essay 
on  the  High  Price  of  Bullion,"  Works,  2d  ed.,  London  (Murray), 
1852,  p.  287.  2  Supra,  Chapter  IV,  §  1. 

'  See  article  by  Robert  Goodbody,  "  More  Gold  means  Higher 
'Time'  Money  and  Lower  Bond  Prices,"  in  The  Gold  Supply  and 
Prosperity,  edited  by  Byron  W.  Holt,  New  York  (The  Moody 
Corporation)  1907,  p.  163  and  after. 


Sec.  1]  DISPERSION   OF   PRICES  189 

The  chief  pecuHarity  of  these  forms  of  property  hes, 
then,  in  the  fact  that  they  are  expressed  in  terms  of 
money  and  therefore  are  compelled  to  keep  in  certain 
peculiar  relations  to  money.  Being  based  on  contracts, 
the  money  terms  of  which  during  a  given  period  must 
not  be  changed,  they  are  not  free  to  be  influenced  in 
the  same  ways  as  other  property.  The  existence  of 
such  contracts  constitutes  one  of  the  chief  arguments 
for  a  system  of  currency  such  that  the  uncertainties 
of  its  purchasing  power  are  a  minimum.  An  uncertain 
monetary  standard  disarranges  contracts  and  discour- 
ages their  formation. 

The  longer  the  contract,  the  larger  the  nonadjusta- 
bility.  A  fifty-year  bond  usually  means  a  relative  fixity 
of  price  for  half  a  century.  Only  at  the  end  of  that 
time,  if  prices  have  risen,  can  bonds,  issued  de  novo 
for  the  means  of  purchasing  goods,  be  correspondingly 
more  numerous  or  of  correspondingly  larger  denomi- 
nations. A  30-days'  bill  of  exchange,  on  the  other 
hand,  while  it  cannot  change  much  in  price,  is  can- 
celed at  the  end  of  a  month.  The  relative  fixity  of 
price  is,  therefore,  of  shorter  duration. 

A  special  class  of  goods,  the  prices  of  which  cannot 
fluctuate  greatly  with  other  prices,  are  those  special 
commodities  which  consist  largely  of  the  money  metal. 
Thus,  in  a  country  employing  a  gold  standard,  the 
prices  of  gold  for  dentistry,  of  gold  rings  and  ornaments, 
gold  watches,  gold-rimmed  spectacles,  gilded  picture 
frames,  etc.,  instead  of  varying  in  proportion  to  other 
prices,  always  vary  in  a  smaller  proportion.  The 
range  of  variation  is  the  narrower,  the  more  predomi- 
nantly the  price  of  the  article  depends  upon  the  gold 
as  one  of  its  raw  materials. 

From  the  fact  that  gold-made  articles  are  thus  more 


190  THE    PURCHASING   POWER   OF  MONEY        [Chap.  IX 

or  less  securely  tied  in  value  to  the  gold  standard,  it 
follows  also  that  the  prices  of  substitutes  for  such 
articles  will  tend  to  vary  less  than  prices  in  general. 
These  substitutes  will  include  silver  watches,  ornaments 
of  silver,  and  various  other  forms  of  jewelry,  whether 
containing  gold  or  not.  It  is  a  fundamental  principle 
of  relative  prices  that  the  prices  of  substitutes  will  move 
in  sympathy.  In  the  case  of  perfect  substitutes,  the 
prices  must  always  be  equal  or  must  bear  a  fixed  ratio 
to  each  other.^ 

The  remaining  items  in  our  list  require  little  comment. 
The  imperfect  adjustability  of  prices  fixed  bylaw  and 
custom  and  the  perfect  adjustability  of  wholesale  prices 
of  commodities  and  prices  of  stocks  are  famihar  to  all. 

^  §2 

The  fact  that  wages,  salaries,  the  price  of  gold  in  non- 
monetary forms,  etc.,  and  especially  the  prices  of  bonded 
securities,  cannot  change  in  proportion  to  monetary 
fluctuations,  means,  then,  that  the  prices  of  other  things, 
such  as  commodities  in  general  and  stocks,  must  change 
much  more  than  in  proportion.  This  supersensitiveness 
to  the  influence  of  the  volume  of  currency  (or  its  velocity 
of  circulation  or  the  volume  of  business)  applies  in  a 
maximum  degree  to  stocks.  Were  a  railroad  to  double 
in  money  value,  the  result  would  be,  since  the  monej' 
value  of  the  bonds  could  not  increase  appreciably,  that 
the  money  value  of  the  stock  would  more  than  double. 
Stocks  are  shares  in  physical  wealth  the  value  of  which, 
in  money,  can  fluctuate.  Since  the  money  price  of 
bonds  is  relatively  inflexible,  that  of  stocks  will  fluctuate 

^  See  Irving  Fisher,  '*  Mathematical  Investigations  in  the  Theory 
of  Value  and  Prices,"  Transactions  of  the  Connecticut  Academy  o} 
Arts  and  Sciences,  1892,  p.  66  and  after. 


Sec.  2]  DISPERSION    OF   PRICES  191 

more  than  the  price  of  the  physical  wealth  as  a  whole. 
The  reason  is  that  these  securities  not  only  feel  the 
general  movement  which  all  adjustable  elements  feel, 
but  must  also  conform  to  a  special  adjustment  to  make 
up  for  the  rigid  nonadjustability  of  the  bonds  associated 
with  them. 

To  illustrate,  let  us  suppose  the  right  side  of  the 
equation  of  exchange  to  consist  of  the  following  ele- 
ments :  — 

Miscellaneous  adjustable  elements  such  as  commodi- 
ties, having  a  value  of $  95,000,000 

Five  thousand  shares  of  stock  at  $1000  per  share, 

making  a  value  of 5,000,000 

Five  thousand  bonds  on  the  same  underljdng  wealth 

at  $1000  each,  making  a  value  of 5,000,000 

Miscellaneous  nonadjustable  elements  such  as  other 
bonds,  notes,  government  salaries,  government 
fees,  dentists'  gold,  etc.,  having  a  value  of  .    .     .        20,000,000 

$125,000,000 

Let  us  suppose  that,  with  no  change  in  the  velocities  of 
currency  circulation  or  in  the  volume  of  business,  there 
is  an  increase  of  40  per  cent  in  the  quantities  of  currency. 
Then,  the  total  value  of  goods  exchanged  will  have 
to  increase  from  $125,000,000  to  $175,000,000.  Let 
us  assume  that  the  last  two  items  are  absolutely  non- 
adjustable;  then  none  of  the  increase  of  $50,000,000 
can  occur  through  any  change  in  these  items,  which  will 
remain  at  $5,000,000  and  $20,000,000,  respectively,  or 
$25,000,000  in  all.  Consequently,  the  first  two  items 
must  rise  by  the  whole  of  the  $50,000,000,  that  is,  from 
$100,000,000  to  $150,000,000  or  50  per  cent.  To  dis- 
tribute this  increase  of  $50,000,000  over  the  first  two 
or  adjustable  items,  let  us  assume  that  the  total  $10,- 
000,000  worth  of  actual  wealth,  which  consists  half  of 


192  THE    PURCHASING   POWER   OF  MONEY        [Chap.  IX 

stocks  and  half  of  bonds,  will  rise  in  the  same  ratio 
as  the  $95,000,000  worth  of  adjustable  elements  rise. 
Now  the  whole  (comprising  all  three  items)  evidently 
rises  from  $105,000,000  to  $155,000,000,  making  an  in- 
crease of  47.6  per  cent.  This,  therefore,  is  the  common 
percentage  which  we  are  to  assume  applies  equally  to 
the  first  item  and  the  combination  of  the  second  and 
third.  Applied  to  the  former  it  makes  an  increase  from 
$95,000,000  to  $140,200,000.  Apphed  to  the  latter  it 
makes  an  increase  from  $10,000,000  to  $14,800,000. 
But  since  half  of  the  property  consists  of  bonds  and 
cannot  increase,  the  whole  of  the  increase,  $4,800,000, 
must  belong  to  the  stock  alone.  This  will,  therefore, 
rise  from  $5,000,000,  to  $9,800,000,  a  rise  of  96  per 
cent.     The  four  items  then  change  as  follows  :  — 

First  item  — from  $95,000,000  to  $140,200,000,  or 
47.6  per  cent. 

Second  item  —  from  $5,000,000  to  $9,800,000,  or 
96  per  cent. 

Third  item  and  fourth  item  —  no  change. 

All  items  combined  —  from  $125,000,000  to  $175,- 
000,000,  or  40  per  cent. 

Besides  the  dispersion  of  price  changes  produced  by 
the  fact  that  some  prices  respond  more  readily  than 
others  to  changes  in  the  factors  determining  price  levels, 
M,  M',  V,  V,  and  the  Q's,  a  further  dispersion  is  pro- 
duced by  the  fact  that  the  special  forces  of  supply  and 
demand  are  playing  on  each  individual  price,  and  caus- 
ing relative  variations  among  them.  Although  these 
forces  do  not,  as  we  have  before  emphasized,  neces- 
sarily affect  the  general  price  level,  they  do  affect  the 
number  and  extent  of  individual  divergencies  above  and 
below  that  general  level.  Each  individual  price  will 
have  a  fluctuation  of  its  own. 


Bcc.  2]  DISPERSION   OP   PRICES  193 

Among  the  special  factors  working  through  supply 
and  demand,  changes  in  the  rate  of  interest  should  be 
particularly  mentioned.  Whether  or  not  due  to  monetary 
changes,  a  movement  of  interest  will  tend  to  make  the 
prices  of  different  things  vary  in  different  directions  or 
to  different  extents.  The  prices  of  all  goods,  the  bene- 
fits of  which  accrue  in  the  remote  future,  depend  on  the 
rate  of  interest.  The  standard  example  is  that  of  bonds 
and  other  securities.  Another  good  example  is  that  of 
real  estate.  In  the  case  of  farm  lands  yielding  a  con- 
stant rental,  a  reduction  of  interest  causes  an  increase 
of  value  in  the  inverse  ratio.  If  interest  falls  from  5 
per  cent  to  4  per  cent,  the  value  will  increase  in  the  ratio 
4  to  5.  If  the  benefits  or  services  are  not  constant  each 
year,  but  are  massed  together  in  the  remote  future,  the 
price  may  be  still  sensitive  to  a  change  in  the  rate  of 
interest.  In  the  case  of  land  used  for  forest  growing 
from  which  the  trees  are  to  be  cut  in  half  a  century, 
the  value  will  be  extremely  sensitive.  A  fall  in  interest 
from  5  per  cent  to  4  per  cent  will  cause  a  rise  of  the 
value  of  the  land,  in  the  ratio  not  of  4  to  5,  but  nearly 
of  4  to  7.^  On  the  other  hand,  mining  land  or  quarries 
with  a  limited  life  will  be  less  sensitive.  The  same 
is  true  of  dwellings,  machinery,  fixtures,  and  other 
durable  but  not  indestructible  instruments,  and  so  on 
down  the  scale  until  we  reach  perishable  and  transient 
commodities,  such  as  food  and  clothing,  which  are  only 
indirectly  affected  by  changes  in  the  rate  of  interest. 

It  is  evident,  therefore,  that  prices  must  constantly 
change  relatively  to  each  other,  whatever  happens  to  their 

1  From  figures  showing  yield  of  forest  of  white  pine  in  New 
Hampshire,  New  Hampshire  Forestry  Commission  Report,  1905-1906, 
p.  246.  See  F.  R.  Fairchild,  "Taxation  of  Timberland,"  Report  of 
the  National  Conservation  Commission,  60th  Congress,  2d  Session, 
Senate  Document  676,  vol.  II,  p.  624. 
o 


194  THE    PURCHASING   POWER   OF  MONEY        [Chap.  IX 

general  level.  It  would  be  as  idle  to  expect  a  uniform 
movement  in  prices  as  to  expect  a  uniform  movement 
for  all  bees  in  a  swarm.  On  the  other  hand,  it  would 
be  as  idle  to  deny  the  existence  of  a  general  move- 
ment of  prices  because  they  do  not  all  move  ahke,  as 
to  deny  a  general  movement  of  a  swarm  of  bees  because 
the  individual  bees  have  different  movements. 

§3 

Corresponding  to  changes  in  an  individual  price  there 
will  be  changes  in  the  quantity  of  the  given  commodity 
which  is  exchanged  at  that  price.  In  other  words,  as 
each  p  changes,  the  Q  connected  with  it  will  change  also ; 
this,  because  usually  any  influence  affecting  the  price 
of  a  commodity  will  also  affect  the  consumption  of  it. 
Changes  in  supply  or  demand  or  both  make  changes  in 
the  quantity  exchanged.  Otherwise  expressed,  the 
point  of  intersection  of  the  supply  and  demand  curve 
may  move  laterally  as  well  as  vertically. 

This  changing  of  the  Q's  introduces  a  new  complica- 
tion. We  have  in  many  of  our  previous  discussions 
been  assuming,  as  was  admissible  theoretically,  that 
all  the  Q's  remain  unchanged  while  we  investigate 
the  changes  in  the  p's  due  to  changes  in  the  currency  or 
in  velocities  of  circulation.  But  practically  we  can 
never  get  an  opportunity  to  study  such  a  case.  Again, 
in  order  to  show  the  effect  of  a  change  in  ''the  volume  of 
business"  upon  the  price  level,  we  supposed  a  case  in 
which  all  the  Q's  were  uniformly  changed.  Such  a 
supposition  is  not  only  impossible  to  carry  out  in  prac- 
tice, but  is  difficult  to  conceive  even  in  theory ;  because, 
as  we  have  just  seen,  each  Q  is  associated  with  a  p.  In 
showing  the  effect  of  a  change  in  the  volume  of  business 
upon  the  level  of  prices  we  cannot  assume  that  all  the 


Sec.  3J  DISPERSION   OF   PRICES  195 

Q's  change  uniformly  in  one  direction  and  all  the  p's 
uniformly  in  the  other.  If  the  first  set  change  uni- 
formly, the  second  cannot  change  uniformly.  A  dou- 
bling in  the  quantities  of  all  commodities  sold,  or  (what 
is  almost  the  same  thing),  a  doubling  of  the  quantities 
consumed,  would  change  their  relative  desirabilities 
and  therefore  their  relative  prices.  To  double  the 
quantity  of  salt  might  make  its  marginal  desirability 
zero,  while  to  double  the  quantity  of  roses  might  scarcely 
lower  their  marginal  desirability  at  all.^ 

We  see,  therefore,  that  it  is  well-nigh  useless  to  speak 
of  uniform  changes  in  prices  (p's)  or  of  uniform  changes 
in  quantities  exchanged  (Q's).  In  place  of  positing 
such  uniform  changes,  we  must  now  proceed  to  the 
problem  of  developing  some  convenient  method  of 
tracing  these  two  groups  of  changes.  We  must  formu- 
late two  magnitudes,  the  price  level  and  the  volume  of 
trade.  This  problem  is  especially  difficult  because,  in 
measuring  changes  in  the  price  level,  we  shall  need 
to  use  the  quantities  (Q's)  in  some  way  as  weights  in 
our  process  of  averaging ;  and  we  now  find,  not  only 
that  the  prices  whose  average  we  seek  are  extremely 
variable,  but  that  the  weights  by  which  we  attempt  to 
construct  the  average  are  variable  also. 

It  is  desired,  then,  in  the  equation  of  exchange,  to 
convert  the  right  side,  ^pQ,  into  a  form  PT  where  T 
measures  the  volume  of  trade,  and  P  is  an  ''index 
number"  expressing  the  price  level  at  which  this  trade 
is  carried  on.  These  magnitudes  —  price  level  (P) 
and  volume  of  trade  (T)  —  need  now  to  be  more  pre- 
cisely formulated.  Especially  does  P  become  hence- 
forth the  focal  point  in  our  study. 

^  Cf.  Jevons,  Theory  of  Political  Economy,  London  (Maemillan), 
1888,  pp.  155-156. 


196  THE   PURCHASING   POWER  OF  MONEY        [Chap.  IX 

As  explained  in  the  next  chapter,  there  are  an  in- 
definite number  of  ways  of  conceiving  and  forming 
index  numbers  of  prices  and  volume  of  trade.  We  shall 
here  mention  only  the  simplest.  T  may  be  conceived  as 
the  sum  of  all  the  Q's,  and  P  as  the  average  of  all  the  p's. 
This  method  is  practically  useful  only  provided  suitable 
units  of  measure  are  selected.  It  must  be  remembered 
that  the  various  Q's  are  measured  in  different  units. 
Coal  is  sold  by  the  ton,  sugar  by  the  pound,  wheat  by 
the  bushel,  etc.  If  we  now  add  together  these  tons, 
pounds,  bushels,  etc.,  and  call  this  grand  total  so  many 
"units"  of  commodity,  we  shall  have  a  very  arbitrary 
summation.  It  will  make  a  difference,  for  instance, 
whether  we  measure  coal  by  tons  or  hundredweights. 
The  system  becomes  less  arbitrary  if  we  use,  as  the  unit 
for  measuring  any  goods,  not  the  unit  in  which  it  is 
commonly  sold,  but  the  amount  which  constitutes  a 
"dollar's  worth"  at  some  particular  year  called  the  base 
year.  Then  every  price,  in  the  base  year,  is  one  dollar, 
and  therefore  the  average  of  all  prices  in  that  year  is 
also  one  dollar.  For  any  other  year  the  average  price 
{i.e.  the  average  of  the  prices  of  the  newly  chosen  units 
which  in  the  base  year  were  worth  a  dollar)  will  be  the 
index  number  representing  the  price  level,  while  the 
number  of  such  units  will  be  the  volume  of  trade. 

The  equation  of  exchange  now  assumes  the  form 

MV  +  M'V  =  PT 

and  its  right  member  is  the  product  of  the  index  number 
(P)  of  prices  multipUed  by  the  volume  of  trade  {T). 

§4 

In  this  chapter  we  have  seen  that  prices  do  not,  and 
in  fact  cannot,  move  in  perfect  unison.     The  reasons 


Sec.  4]  DISPERSION   OP  PRICES  197 

for  dispersion  are  principally  three:  (1)  Many  prices 
are  restrained  by  previous  contract,  by  legal  prohibition, 
or  by  force  of  custom.  (2)  Some  prices  are  intimately 
related  to  the  money  metal.  (3)  Each  individual  price 
is  subject  to  special  variation  under  the  influence  of  its 
particular  supply  and  demand.  There  exists,  however, 
a  compensation  in  price  movements  in  the  sense  that  the 
failure  of  one  set  of  prices  to  respond  to  any  influence 
on  the  price  level  will  necessitate  a  correspondingly 
greater  change  in  other  prices. 

The  quantities  sold  likewise  vary,  and  their  variations 
are  bound  up  with  those  of  prices. 

In  order  to  express  in  one  figure  the  general  movement 
of  prices,  an  index  number  (P)  is  constructed ;  and 
in  order  to  express  in  one  figure  the  general  movement  of 
trade,  an  index  of  trade  (T)  is  constructed.  The  nature 
of  these  indices  will  form  the  subject  of  the  next  chapter. 


CHAPTER  X 

THE   BEST  INDEX  NUMBERS  OF   PURCHASING   POWER 

§1 

In  the  previous  chapter  the  necessity  for  an  index 
number  (P)  was  shown  and  a  particular  form  of  index 
number  was  suggested.  This  form  of  index  number 
had  been  shown  in  Chapter  II  and  its  appendix  to  meet 
certain  conditions  (of  proportionality  of  price  level  to 
quantity  of  money,  etc.)  required  by  the  equation  of 
exchange,  MV+M'V'  =  PT,  In  the  present  chapter, 
this  index  number  will  be  compared  with  others  and 
the  general  purposes  of  index  numbers  discussed,  in- 
cluding purposes  having  little  direct  concern  with  the 
equation  of  exchange. 

Index  numbers  may  be  compared  in  respect  to  (1) 
form,  under  which  term  are  included  methods  of  weight- 
ing and  of  determining  the  "base"  prices;  (2)  the 
selection  of  elements  to  be  included.  In  this  section 
we  shall  consider  the  question  of  form. 

The  number  of  possible  forms  of  index  numbers  is 
infinite.  They  differ  enormously  in  complexity,  in  ease 
of  calculation,  and  in  conformity  to  various  other  tests. 
A  few  of  the  simplest  may  here  be  mentioned.  Their 
discussion  will  be  brief  and  will  in  many  cases  be  dog- 
matic. Full  proofs  and  discussions  are  contained  in 
the  mathematical  appendix.^ 

If  in  1900  the  average  price  per  pound  of  sugar  was 
6  cents,  and  in  1910  it  was  8  cents,  the  ratio  of  the  price 

1  See  Appendix  to  (this)  Chapter  X,  §§  1-8,  where  44  types  of 
index  numbers  are  compared. 

198 


Sec.  1]  THE   BEST  INDEX  NUMBERS  199 

in  1910  to  that  in  1900  must  have  been  f  or  133^  per 
cent.  If,  in  the  same  period,  the  average  price  of  coal 
per  ton  had  changed  from  $4  to  $6,  the  corresponding 
ratio  for  coal  must  have  been  |  or  150  per  cent.  If  the 
price  of  a  given  grade  of  cloth,  on  the  other  hand,  fell 
from  10  cents  to  8  cents  a  yard,  the  ratio  for  cloth  must 
have  been  ^q  or  80  per  cent.  P  is  an  average  of  all 
these  three  price  ratios  and  other  price  ratios,  that  is, 
an  average  of  133^  per  cent,  150  per  cent,  80  per  cent, 
etc.  The  simple  arithmetical  average  of  these  three 
ratios  specified  would  be  imfo  +  i50%+S0fo  ^  or  121 

per  cent.  The  simple  geometric  average  would  be 
-v/l33i  X  150  X  80,  or  117  per  cent. 

These  are  examples  of  simple  or  unweighted  averages. 
Since,  however,  weighted  averages  have  many  advan- 
tages in  theory  and  some  advantages  in  practice,  we 
shall  proceed  to  consider  them. 

There  are  innumerable  methods  of  weighting  ^  and  of 
averaging.  None  of  them  is  perfectly  satisfactory 
from  a  theoretical  standpoint.  We  must  choose  what 
seems  to  be  best  from  a  practical  standpoint.  The 
effect  of  changed  volume  of  currency  or  changed  veloc- 
ity of  circulation  on  the  whole  series  of  prices  is  complex, 
and  cannot,  even  in  theory,  be  compressed  into  one 
figure  representing  all  price  changes,  any  more  than  a 

1  For  discussions  of  different  ways  that  have  been  proposed, 
see  Walsh,  The  Measurement  of  General  Exchange  Value,  New  York 
and  London  (Maemillan),  1901  ;  Edgeworth,  "Report  on  Best 
Methods  of  Ascertaining  and  Measuring  Variations  in  the  Value  of 
the  Monetary  Standard"  ;  Report  of  the  British  Association  for  the 
Advancement  of  Science  for  1887,  pp.  247-301 ;  ditto  for  1888,  pp. 
181-209  ;  ditto  for  1889,  pp.  133-164.  Nitti,  La  misura  delle  varior 
zioni  di  valore  delta  moneta,  Turin,  624  pp. ;  also  the  Appendix  to 
(this)  Chapter  X. 


200  THE   PURCHASING    POWER  OF  MONEY      [Chap.  X 

lens  can  be  constructed  which  will  focus  in  one  point 
all  the  rays  of  light  reaching  it  from  a  given  point. 
But,  although  in  the  science  of  optics  we  learn  that  a 
perfect  lens  is  theoretically  impossible,  nevertheless,  for 
all  practical  purposes  lenses  may  be  constructed  so 
nearly  perfect  that  it  is  well  worth  while  to  study  and 
construct  them.  So,  also,  while  it  seems  theoretically 
impossible  to  devise  an  index  number,  P,  which  shall 
satisfy  all  of  the  tests  we  should  like  to  impose,^  it  is, 
nevertheless,  possible  to  construct  index  numbers  which 
satisfy  these  tests  so  well  for  practical  purposes  that  we 
may  profitably  devote  serious  attention  to  the  study 
and  construction  of  index  numbers. 

The  index  number  mentioned  in  Chapter  IX  may  be 
constructed  by  the  following  process:  Suppose  that  the 
year  1910  is  the  period  to  be  considered  in  our  equation 
of  exchange  MV  +  M'V  =  ^pQ  =  PT.  We  select 
another  year  (say  1900)  and  call  it  the  "  base  "  year. 
This  means  that  the  prices  of  1910  are  to  be  expressed 
as  a  percentage  of  the  prices  of  the  equation  of  exchange 
for  1900. 

Next  we  obtain  an  expression  for  trade  (or  T). 
As  shown  in  the  appendix  to  this  chapter,  every  form 
of  index  number,  P,  for  prices  implies  a  correlative 
form  of  index  for  trade,  T,  and  vice  versa.  It  is  con- 
venient to  select  T  first.  We  observe  that  trade  (or  T) 
is  not  the  value  of  transactions  measured  at  the  actual 
prices  of  the  year  1910,  for  this  value  is  PT  or  2pQ, 

1  Cf.  Mill,  Political  Economy,  Book  III,  Chapter  XV ;  Sidgwick, 
Principles  of  Political  Economy,  Book  I,  Chapter  II ;  "Report  of 
Committee  on  Value  of  Monetary  Standard,"  Report  of  the  British 
Association  for  the  Advancement  of  Science,  1887  ;  Wesley  C.  Mitchell, 
Gold,  Prices,  and  Wages  under  the  Greenback  Standard,  Berkeley,  1908 
(University  of  California  Press),  p.  19;  and  Appendix  to  (this) 
Chapter  X. 


Sec.  1]  THE   BEST  INDEX   NUMBERS  201 

that  is,  the  entire  right  side  of  the  equation.  Trade 
(T)  by  itself  must  be  divorced  from  the  price  level  (P) ; 
it  may  be  conceived  as  the  value  which  the  total  trans- 
actions would  have  had  if  the  actual  quantities  sold  had 
been  sold  at  the  base  prices.  It  is  thus  the  sum  of  a 
number  of  terms,  each  term  being  the  product  of  the 
quantity,  or  Q,  pertaining  to  1910  and  the  price,  or  p, 
pertaining  to  the  base  year  1900.  Algebraically  it  is 
Pi>Q  +  p'oQ'  +  p'\Q"  +  etc.,  or,  more  briefly,  ^PoQ,  where 
the  prices  of  1910  are  expressed  simply  as  p,  p',  p", 
etc.,   and  those  of  the  base  year,  1900,  are  expressed 

as  Po^  V\j  P"o,  etc. 

Having  defined  this  ideal  value  (T),  we  now  define 
P  as  the  ratio  of  the  real  value  of  transactions  in  1910 
(2pQ)  to  that  ideal  (2poQ).  More  fully  expressed,  P  is 
the  ratio  of  a  real  value  (the  value  of  the  trade  of 
1910  at  the  prices  of  1910)  to  an  ideal  value  (the  value 
of  the  trade  of  1910  at  the  prices  of  1900).  This  ratio 
is  really  a  weighted  arithmetical  average  of  price  ratios.^ 
The  foregoing  method  is  simple  both  in  conception  and 
in  mathematical  expression, ^  and  appears  to  furnish, 
theoretically  at  least,  the  best  form  of  P,  or  index  num- 
ber of  prices.  The  particular  form  of  P  (viz.  2pQ  -h 
2poQ)  which  we  have  just  described  is,  then,  associated 
with  and  dependent  on  a  particular  form  of  T  (viz. 
2poQ).  T  msbj  be  called  an  index  number  of  trade,  and 
we  may  say  that  the  particular  form  of  T  (viz.  2p„Q) 
is  the  best  form  of  index  or  barometer  of  trade. 

Another  method  of  conceiving  the  same  form  of 
index  number  of  prices  is  that  mentioned  at  the  close  of 

*  See  Appendix  to  (this)  Chapter  X  for  a  table  and  discussion 
of  forty-four  sample  types  of  index  numbers. 

■^  It  is  formula  11  of  the  large  table  in  the  Appendix  to  (this) 
Chapter  X. 


202  THE    PURCHASING   POWER   OF  MONEY      [Chap.  X 

the  preceding  chapter,  as  follows:  Conceive  each  kind 
of  goods  to  be  measured  in  a  new  physical  unit  —  viz. 
the  amount  which  was  worth  one  dollar  in  the  base 
year  (1900)  —  and  let  us  use  this  unit  for  each  other  year 
(as  1910).  Thus  instead  of  a  pound  as  the  unit  for 
sugar  we  take  as  the  unit  whatever  amount  of  sugar  was 
a  dollar's  worth  in  1900.  Hence  the  price  of  sugar  in 
the  base  year,  1900,  was  $1,  as  of  course  was  the  price 
of  everything  else.  If,  now,  the  price  of  sugar  in  any 
other  year  (as  1910)  is  $1.25  in  terms  of  the  new  unit 
(viz.  the  amount  which  was  a  dollar's  worth  in  1900), 
we  know  that  the  price  has  risen  25  per  cent.  In  this 
way  P  may  be  defined  simply  as  an  average  price  instead 
of  as  an  average  price  ratio  and  T  as  the  total  number 
of  the  new  units  of  goods  sold  of  all  kinds.  The  right 
side  of  the  equation  is  now  simply  the  product  of  the 
total  number  of  units  sold,  multiplied  by  their  average 
price. 

The  two  definitions  of  P  which  have  been  given  (viz. 
the  ratio  of  real  to  ideal  values,  and  the  average  price  in 
1910  of  all  goods  when  measured  in  dollar's  worth  of 
1900)  are  interchangeable ;  and  both  definitions  of  T 
(ideal  values  of  transactions  in  1910  at  prices  of  1900,  and 
total  number  of  units  sold  in  1910,  the  units  being 
each  a  dollar's  worth  in  1900)  are  interchangeable. 
There  are  other  ways  of  defining  P  and  T  without  chang- 
ing their  meanings.  Thus  ''P  is  the  weighted  arith- 
metical average  of  the  ratios  of  prices  of  goods  in  1910 
to  those  of  1900,  when  these  ratios  are  weighted  accord- 
ing to  the  values  of  the  goods  exchanged  in  1910  reck- 
oned at  the  prices  of  1900."  Whichever  of  these  defi- 
nitions we  prefer,  the  system  of  index  numbers  is  the 
same  and  has  advantages  over  most  other  systems. 
Above  all,  it  enables  us  to  say  without  qualification  that 


Sec.  1]  THE   BEST   INDEX  NUMBERS  203 

if  the  quantities  sold  remain  unchanged,  so  that  T  will 
remain  unchanged,  P  will  vary  directly  as  the  left  side 
of  the  equation  of  exchange.^ 

We  choose,  then,  as  one  of  the  best  index  numbers  of 
prices,  the  average  price  of  the  goods  sold,  those  goods 
being  measured  in  units  worth  a  dollar  in  the  base  year; 
in  other  words,  the  ratio  of  the  value  of  sales  at  actual 
prices  to  the  value  of  the  same  sales  if  made  at  base 
prices ;  in  still  other  words,  the  weighted  arithmetical 
average  of  all  price  ratios,  each  ratio  being  weighted 
according  to  the  values  sold,  reckoned  at  base  prices. 

We  have  still  to  consider  the  selection  of  the  base.  It 
makes  a  difference  to  the  above  index  numbers,  not 
only  absolutely,  but  also  relatively,  whether  the  base 
year  is,  for  instance,  1900  or  1860. 

Excepting  Jevons's  index  numbers,  which  were 
geometric  averages,  there  are  few  index  numbers  which 
are  not  vitiated  in  some  degree  by  having  a  base  remote 
from  the  years  for  which  comparisons  are  most  needed. 
As  Professor  Marshall  has  maintained  and  as  Professor 
Flux  has  emphasized,  the  best  base  for  any  year  seems 
to  be  the  previous  year. 

Instead,  then,  of  employing  a  fixed  base  year  for  which 
all  prices  are  called  100  per  cent  and  in  terms  of  which  all 
other  prices  are  expressed  in  percentages,  each  year 
may  be  taken  as  the  base  for  the  succeeding  year. 
Thus  we  obtain  a  chain  of  mdex  numbers,  each  num- 
ber being  connected  with  the  preceding  year  instead  of 
with  a  common  base  year. 

The  great  advantage  of  this  chain  system  is  that  it 
yields  its  best  comparison  for  the  cases  in  which  com- 
parison is  most  used  and  needed.  Each  year  we  are  inter- 

'  See  Appendix  to  Chapter  II  and  the  Appendix  to  (this)  Chap- 
ter X,  §§  5,  6,  7. 


204  THE    PURCHASING   POWER  OF  MONEY       [Chap.  X 

ested  in  Sauerbeck's  index  number  in  order  to  compare 
it  with  the  number  of  the  preceding  year,  and  only  to  a 
less  extent  with  other  years.  The  number,  however,  as 
actually  constructed,  affords  something  quite  different. 
It  gives  us,  as  its  best  or  most  accurate  comparison, 
the  ratio  between  the  current  year  and  the  years  1867- 
1877.  This  comparison  is  of  little  or  no  interest  to 
any  one.  What  all  users  of  these  statistics  actually  do 
is  to  compare  two  comparisons.  The  index  numbers  for 
1909  and  1910  (each  calculated  in  terms  of  1867-1877) 
are  compared  with  each  other.  But  direct  comparison 
between  1909  and  1910  would  give  a  different  and  more 
valuable  result.  To  use  a  common  base  is  like  compar- 
ing the  relative  heights  of  two  men  by  measuring  the 
height  of  each  above  the  floor,  instead  of  putting  them 
back  to  back  and  directly  measuring  the  difference  of 
level  between  the  tops  of  their  heads.  The  direct  com- 
parison is  more  accurate,  although  in  the  case  of  the 
men's  heights  both  methods  would  theoretically  agree. 
In  the  case  of  price  levels,  unfortunately,  few  index 
numbers  will  even  theoretically  give  consistent  results 
when  the  base  is  shifted ;  ^  and  those  few  will  fail  to 
meet  other  equally  important  tests. 

It  may  be  said  that  the  cardinal  virtue  of  the  suc- 
cessive base  or  chain  system  is  the  facility  it  affords  for 
the  introduction  of  new  commodities,  the  dropping  out 
of  obsolete  commodities,  and  the  continual  readjustment 
of  the  system  of  weighting  to  new  conditions.  A  fixed 
base  system  soon  gets  behind  the  times  in  every  sense 
of  the  word. 

§2 

Our  next  question  is  :  What  prices  should  be  selected 
in  constructing  an  index  number  ?     The  answer  to  this 

1  See  Appendix  to  (this)  Chapter  X,  §  5,  test  7. 


Sec.  2]  THE   BEST  INDEX  NUMBERS  205 

question  largely  depends  on  the  purpose  of  the  index 
number.  Hitherto  we  have  considered  only  one  purpose 
of  an  index  number,  viz.  to  best  meet  the  requirements 
of  the  equation  of  exchange.  But  index  numbers  may 
be  used  for  many  other  purposes,  of  which  the  two 
chief  are  to  measure  capital  and  to  measure  income. 
Each  of  the  three  purposes  mentioned  (viz.  exchange, 
capital,  and  income)  may  be  subclassified  according  as 
the  comparison  desired  is  between  places  or  times.  Thus 
mdex  numbers  may  be  used  for  comparisons  between 
places  with  respect  to  their  exchange  of  goods,  their 
capital,  or  their  income.  When,  for  instance,  the  British 
Board  of  Trade  ^  tries  to  compare  the  cost  of  living  in 
various  towns  of  England,  Germany,  and  the  United 
States  the  comparison  is  with  reference  to  the  prices  of 
living  (or  income)  of  the  working  classes. 

We  thus  have  at  least  six  large  classes  of  purposes 
for  which  index  numbers  may  be  used,  viz.  to  compare 
the  prices,  in  different  places,  of  the  goods  exchanged ;  of 
the  capital  goods;  and  of  the  income  goods;  and  of  the 
same  three  groups  of  goods  at  different  times. 

In  each  of  the  six  cases,  prices  of  goods  and  quantities 
of  goods  will  be  associated  with  each  other,  and  an  index 
number  (P)  for  one  will  imply  an  index  number  (T)  for 
the  other  (we  here  use  T  in  the  general  sense  of  an  index 
of  quantities  of  goods  whether  they  are  exchanged  goods, 
as  hitherto,  or  capital  goods,  or  income  goods). 

Evidently  there  will  be  a  great  difference  in  the  selection 
of  the  prices  to  be  compared  according  to  which  of  the 
six  comparisions  we  wish  to  make.  Suppose,  for  in- 
stance, that  we  wish  to  measure  changes  in  the  general 

*  See  Report  (to  Parliament)  of  an  Enquiry  hy  the  Board  of  Trade 
into  Workinci  Class  Rents,  Housing  and  Retail  Prices,  London 
(Darling),  1908,  1909. 


206  THE    PURCHASING    POWER   OF   MONEY       [Chap.  X 

level  of  prices  of  capital  goods/  —  railways,  ships,  real 
estate,  etc.,  —  and  also  to  measure  the  relative  changes 
in  the  amounts  of  those  goods.  The  prices  of  some  kinds 
of  capital  may  have  increased,  and  of  others  decreased, 
and  some  may  have  increased  at  different  rates  from 
others.  How  shall  we  measure  the  general  change  in 
prices  of  capital  goods  ?  Again,  the  quantity  of  some 
kinds  of  capital,  as  railroads,  may  have  increased  faster 
than  that  of  other  kinds,  as  sailing  ships.  Still  other 
kinds  of  capital  may  have  decreased.  How  shall  it  be 
determined  whether  capital  in  general  has  increased,  and 
how  much  ?  These  two  problems  (of  prices  of  capital 
and  quantities  of  capital)  may  be  said  to  consist  in 
measuring  the  average  change  in  the  price  of  the  same 
quantity  of  capital,  and  the  average  change  of  quantity 
of  capital  taken  at  the  same  prices. 

For  either  index  (since  only  capital  is  under  considera- 
tion, and  not  income  or  other  designated  goods,  whether 
stocks  or  flows),  the  index  numbers  should  relate,  not 
to  general  prices  and  quantities,  but  only  to  prices  and 
quantities  of  capital  goods.  Thus,  the  prices  and  quan- 
tities of  all  labor  services  should  be  omitted.  The  use 
of  capital  and  the  rents  paid  for  that  use,  such  as  the 
rent  paid  for  house  shelter,  should  be  omitted.  Only 
capital  instruments,  and  not  the  services  yielded  by 
these,  should  be  included.  We  may  obtain  the  price 
index  first  and  then  obtain  a  quantity  index  by  dividing 
the  value  of  capital  in  any  year  by  the  price  index,  or  we 
may  proceed  in  the  reverse  direction.^  In  making  index 
numbers  of  prices  of  capital  and  quantities  of  capital,  we 

1  This  has  been  suggested  by  Nicholson,  Journal  of  the  Royal 
Statistical  Society,  March,  1887. 

2  Giffen,  in  his  Growth  of  Capital,  London  (Bell  &  Sons),  1899, 
pp.  50-54,  makes  correction  for  price  changes  although  without 
attempting  to  construct  a  special  index  number  for  capital. 


Sec.  2]  THE   BEST  INDEX   NUMBERS  207 

naturally  select  for  our  list  articles  which  are  important 
as  capital,  and  weight  them  accordingly. 

To  determine  this  general  change  in  prices  of  capital, 
we  should  weight  each  ratio  by  the  value  of  the  partic- 
ular capital  to  which  that  ratio  relates.  In  this  case 
each  ratio  should  be  weighted,  not  according  to  the 
annual  sales,  but  according  to  the  existing  capital. 
Obviously,  the  difference  between  these  two  modes  of 
weighting  may  be  great.  Thus,  real  estate  forms  a 
large  part  of  all  existing  capital,  but  sales  of  real  estate 
are  a  relatively  unimportant  part  of  all  sales.  Food 
products,  on  the  other  hand,  contribute  little  to  capital 
and  much  to  exchange.  Consequently,  prices  and  quan- 
tities of  food  products  would  not  figure  in  capital  index 
numbers,  but  would  figure  largely  in  the  index  numbers 
relating  to  the  equation  of  exchange. 

Again,  suppose  the  purpose  of  the  index  numbers  of 
prices  is  to  measure  the  quantities  and  prices  of  income, 
not  of  elements  of  capital.  In  this  case  the  list  of 
articles  and  their  weights  will  be  quite  different  from 
those  in  a  capital  index. 

If  the  income  of  workingmen  is  under  consideration, 
we  have  to  deal  with  index  numbers  for  prices  of  those 
goods  entering  into  workingmen's  budgets,  and  with 
index  numbers  of  the  quantities  of  such  goods.  The 
first  will  show  the  cost  of  living  of  the  workingman, 
or  the  purchasing  power  of  a  workingman's  dollar; 
the  second  will  show  what  is  called  his  "real  wages" 
or  ''consumption."  In  this  case  the  aim  is  to  compare, 
not  stocks  existing  at  two  points  of  time,  but  flows 
through  two  periods  of  time.  One  way  to  obtain  an 
index  of  real  wages  is  to  correct  the  nominal  or  money 
wages  by  using  the  index  number  of  prices  of  goods 
for  which  wages  are  spent.     Thus,  if  money  wages  for 


208  THE    PURCHASING   POWER   OF  MONEY       [Chap.  X 

1908  were  twice  those  for  1900,  but  money  prices  of  the 
necessaries  and  comforts  of  life  had  also  doubled,  real 
wages  would  be  unchanged. 

Evidently  the  index  numbers  used  in  the  case  of 
quantities  and  prices  of  workmen's  living  are  not  the 
same  as  those  used  in  the  case  of  capital.  Goods  should 
have  each  an  importance  in  the  index  number,  depend- 
ent upon  its  importance  in  workingmen's  budgets. 
The  goods  in  this  case  are  flows,  while  in  the  case  of 
capital  the  goods  considered  were  stocks.  In  compar- 
ing capital,  the  index  numbers  must  relate  to  capital ; 
and  in  comparing  income,  the  index  numbers  must 
relate  to  income. 

§3 

Perhaps  the  most  important  purpose  of  index  num- 
bers is  to  serve  as  a  basis  of  loan  contracts.^     It  is 

^  An  early  attempt  to  construct  a  series  of  index  numbers  ex- 
pressing the  general  change  in  prices  was  made  by  Sir  George 
Shuckburgh  Evelyn,  Bart.,  F.R.S.  and  A.S.  in  1798  in  an  article 
entitled  "An  Account  of  Some  Endeavors  to  Ascertain  a  Standard 
of  Weight  and  Measure,"  in  the  Philosophical  Transactions  of  the 
Royal  Society  of  London,  Vol.  LXXXVIII,  pp.  133-182,  inclusive. 

Bishop  William  Fleetwood  in  1707  in  Chronicon  Preciosum,  an 
Account  of  English  Money,  the  Price  of  Corn  and  Other  Commodities 
for  the  Last  Six  Hundred  Years,  raises  and  discusses  the  question 
whether  the  holder  of  a  fellowship  founded  between  1440  and  14G0 
and  open  only  to  persons  having  an  estate  of  less  value  than  £5  a 
year  may  rightly  swear  that  he  has  less  than  that,  if  he  has  £6,  the 
value  of  money,  however,  having  meanwhile  greatly  depreciated. 

The  idea  of  using  an  index  number  or  tabular  standard  of  money 
value  was  later  put  forth  by  Joseph  Lowe,  The  Present  State  of  Eng- 
land in  regard  to  Agriculture  and  Finance,  London,  1822  (see  pp. 
261-291,  Appendix,  pp.  89-101),  and  afterwards  by  G.  Poulett 
Scrope,  Principles  of  Political  Economy  .  .  .  applied  to  the  Present 
State  of  Britain,  London,  1833,  pp.  405-408,  although,  as  we  have 
seen,  the  idea  of  an  index  number  itself  antedated  them.  See  Correa 
Moylan  Walsh,  The  Measurement  of  General  Exchange  Value,  New 
York  and  London  (Macmillan),  1901 ;  Bibliography,  p.  555. 


Sec.  3J  THE   BEST  INDEX   NUMBERS  209 

desirable  to  determine  the  particular  forra  and  weighting 
best  suited  to  this  purpose  as  well  as  the  best  selection 
of  prices  to  be  included. 

An  index  number  which  serves  the  purpose  of  measur- 
ing the  appreciation  or  depreciation  of  loan  contracts  — 
or  what  is  called  "  deferred  payments  "  —  evidently  be- 
longs to  the  time  rather  than  the  place  group  of  com- 
parisons. But  to  which  if  any  of  the  three  sub-groups 
(exchange,  capital,  or  income)  it  most  properly  belongs 
is  not  at  first  clear.  But,  before  considering  this  ques- 
tion and  as  a  preliminary  to  finding  the  best  index 
number  for  contracts  between  borrower  and  lender,  we 
must  arrive  at  some  opinion  as  to  what  is  the  ideal 
basis  for  loan  contracts. 

In  the  first  place,  it  should  be  pointed  out  that 
though  there  is  a  gain  and  loss  there  is  not  necessarily 
any  ''injustice"  wrought  because  of  a  change  in  the 
level  of  prices.  Thus,  if  a  man  borrows  $1000,  con- 
tracting to  pay  it  back  with  $40  additional  as  interest 
at  the  end  of  five  years,  and  meanwhile  prices  unex- 
pectedly double,  he  is  a  decided  gainer.  Though  he 
has  to  pay,  to  be  sure,  the  same  number  of  dollars,  he 
needs  to  sell  only  about  half  as  much  of  his  stock  of 
goods  as  he  expected.  He  pays  back,  in  the  princi- 
pal, only  half  of  the  real  purchasing  power  borrowed. 
The  lender,  on  the  other  hand,  is  a  loser  by  the  change. 

Yet  the  contract  was  perfectly  fair.  Each  party 
knew  or  should  have  known  that  the  price  level  might 
change,  and  took  the  risk.  There  was  no  fraud  any 
more  than  when  wheat  has  been  ordered  for  future 
delivery  at  a  certain  price  and  the  market  unexpectedly 
turns;  or  when  an  insurance  company  loses  a  ''risk" 
prematurely. 

Indeed,  for  a  government  to  attempt  by  legislation 


210  THE    PURCHASING   POWER   OF   MONEY       [Chap.  X 

to  deprive  the  gainer  of  his  profit  would  itself  be  in 
general  unfair.^  To  protect  themselves  from  losses 
the  risk  of  which  they  took  upon  themselves,  the  losing 
parties  cannot  justly  betake  themselves  to  legislation 
after  the  making  of  contracts. 

The  unfairness  of  so  doing  becomes  the  more  manifest, 
when  it  is  considered  that,  if  the  change  in  price  level 
is  at  all  expected,  there  is  apt  to  be  some  compensation 
by  means  of  an  adjustment  in  the"  rate  of  interest.^ 
If  the  price  level  is  rising,  the  nominal  rate  of  interest 
will  probably  be  a  little  higher,  compensating  the 
lender  somewhat  for  the  loss  of  part  value  in  his  prin- 
cipal ;  while,  if  the  price  level  is  falling,  the  borrower 
is  likely  to  be  partly  compensated  for  his  loss  by  a 
lower  nominal  rate  of  interest.  It  is  not  right  that 
either  side  should  use  its  influence  with  government 
to  impair  the  obligations  of  contracts  already  made.^ 
It  is,  however,  sound  public  policy  to  lessen  in  advance 
the  risk  element,  as  rapidly  as  may  be,  so  that  future 
contracts  may  be  made  by  all  parties  on  the  most  cer- 
tain basis  possible.  In  the  problem  of  time  contracts 
between  borrowers  and  lenders,  the  ideal  is  that  neither 
debtor  nor  creditor  should  be  worse  off  from  having 
been  deceived  by  unforeseen  changes.  Experience 
shows  that  the  rate  of  interest  will  seldom  adjust  itself 
perfectly  to  changes  in  price  level,  because  these  changes 
are  only  in  part  foreseen.  The  aim  should  be  to  make 
the  currency  as  certain  or  dependable  as  possible. 
Practically  speaking,  this  means  that  it  shall  be  as 
nearly  constant  as  possible. 

^  Cf.  Irving  Fisher,  "Appreciation  and  Interest,"  Part  3,  Publican 
tions  of  the  American  Economic  Association,  1896. 
^  Rate  of  Interest,  Chapter  XIV. 
'  Appreciation  and  Interest,  Part  3,  §  4. 


Sec.  3]  THE   BEST  INDEX  NUMBERS  211 

In  an  ideal  standard  of  value,  the  index  number  of 
prices  would  continually  register  100  per  cent.^  But 
as  long  as  an  absolutely  stable  currency  does  not  exist, 
and  cannot  be  had,  the  index  number  is  itself  a  possible 
standard  for  long-time  contracts.  It  is  called  the 
''tabular  standard,"  as  it  depends  on  a  table  of  prices. 
Thus,  if  a  man  borrows  $1000  when  the  index  number 
is  100,  he  might  agree  to  pay  back,  not  the  same  dollars, 
but  the  same  general  purchasing  power,  with  interest. 
If,  at  the  time  of  repayment,  the  index  number  had  gone 
to  150,  the  principal  of  the  debt  would  be  understood 
to  be  $1500,  since  this  represents  the  same  purchasing 
power  that  was  borrowed.  If,  on  the  other  hand,  the 
level  of  prices  had  fallen  to  80,  the  principal  would 
automatically  become  $800.  Thus,  both  parties  would 
be  protected  against  fluctuations  in  the  value  of  money. 
The  same  correction  would  apply  to  the  interest  pay- 
ments, each  of  which  would  be  adjusted  according  to 
the  index  number  relating  to  the  time  of  payment. 

We  are  now  ready  to  consider  the  question  of  what 
are  the  goods  the  prices  of  which  should  be  included  in 
an  index  number  to  serve  the  purposes  of  measuring 
changes  in  loan  contracts. 

'  It  has  been  argued  that  an  ideal  standard  ought  to  be  such 
as  to  keep  constant  not  objective,  but  subjective,  prices,  so  that  a 
debt  would  be  repaid  in  a  given  amount  of  "labor"  or  "utility." 
But,  aside  from  the  practical  difficulties  of  measuring  such  subjec- 
tive magnitudes  —  which  are  insuperable  and  therefore  render  their 
discussion  purely  academic  —  there  are  even  more  serious  theo- 
retical objections  because  of  the  fact  that  the  standard  would  in- 
crease with  some  persons  and  decrease  with  others  as  they  grow 
poorer  or  richer  and  that  these  changes  are  anticipated  in  making 
loan  contracts  —  in  fact,  are  the  instigating  causes  of  such  contracts. 
See  §  4  infra  and  Irving  Fisher,  "Appreciation  and  Interest," 
Chapter  XII,  §  2,  Publications  of  the  American  Economic  Associa' 
Hon,  1896. 


212  THE    PURCHASING    POWER   OF   MONEY       [Chap.  X 

If  all  goods  kept  the  same  ratios  of  prices  among 
themselves,  it  would  make  no  difference  whether  a 
loan  contract  were  made  in  terms  of  one  index  number  or 
another  or  even  whether  it  were  made  in  terms  of  wheat, 
tons  of  coal,  or  pounds  of  sugar.  But  because  prices 
do  not  vary  in  the  same,  but  in  different  proportions,  an 
index  number  measuring  the  general  level  of  prices  is 
necessary.  If  repayment  is  made  in  equivalent  pur- 
chasing power  (plus  interest),  over  one  kind  of  goods, 
this  may  be  either  more  or  less  than  equivalent  purchas- 
ing power  over  other  kinds.  Hence,  one  party  or  the 
other  is  a  loser  according  to  the  kind  of  goods  he  handles 
as  a  producer  or  prefers  to  use  as  a  consumer.  Even 
if  each  contracting  party  could  arrange  to  receive  or  pay 
back  purchasing  power  over  an  amount  of  goods  of  the 
kinds  which  most  concerned  him,  equivalent  to  what  he 
lent  or  borrowed,  with  interest,  the  speculative  element 
resulting  in  gain  or  loss  to  one  or  the  other,  though  de- 
creased, would  not  be  entirely  removed.^ 

Suppose,  for  example,  that  a  lender  receives  back 
purchasing  power  over  an  amount  of  goods  of  the  kinds 
he  wished  to  use,  equivalent  to  what  he  lent  plus  in- 
terest.2  Suppose  also  that,  during  the  period  of  the 
loan,  these  goods  appreciate  relatively  to  others. 
Then  the  lender  really  gains,  since  he  can  now  get  more 
of  other  goods  in  exchange  for  those  it  was  his  original 
purpose  to  use,  —  a  course  which  he  may  now  be 
tempted  to  take  while  otherwise  he  would  not.  To  the 
borrower,  however,  the  appreciation  of  the  goods   on 

1  Cf.  Kinley,  Money,  New  York  (Maemillan),  1904,  p.  267. 

^  The  argument  of  the  remainder  of  this  section  is  substantially 
the  same  as  that  in  a  paper  by  Harry  G.  Brown,  in  the  Quarterly 
Journal  of  Economics,  August,  1909,  entitled,  "A  Problem  in  De- 
ferred Payments  and  the  Tabular  Standard." 


Sec.  3]  THE   BEST  INDEX  NUMBERS  213 

the  basis  of  which  repayment  is  made,  relatively  to  the 
goods  he  is  engaged  in  producing,  might  be  regarded 
as  causing  him  loss.  The  same  purchasing  power  over 
the  goods,  on  the  basis  of  which  he  is  to  make  pay- 
ment, means  in  such  a  case,  a  greater  purchasing  power 
over  the  goods  he  is  engaged  in  producing. 

It  is  clear  that  no  one  kind  of  goods  is  a  fair  stand- 
ard. An  index  number  intended  to  serve  as  a  standard 
for  deferred  payments  must  have  a  broad  basis. 

Were  all  borrowers  and  all  lenders  interested  merely 
as  consumers  —  lenders  denying  themselves  in  immedi- 
ate consumption  in  order  to  lend,  with  the  idea  of  con- 
suming more  on  repayment,  and  borrowers  planning  to 
consume  more  immediately  with  the  intention  of  later 
consuming  less  —  an  exactly  satisfactory  index  number 
for  each  individual  would  seem  impossible.  The  goods 
which  interested  a  lender  in  any  given  case  might  not  be 
those  of  most  importance  to  the  borrower.  Only  a 
rough  average  could  be  struck  and  an  index  number 
found  to  be  used  by  all  parties  in  their  contracts.  Such 
an  average  would  doubtless  be  one  in  which  each  price 
ratio  would  be  weighted  according  to  the  total  con- 
sumption of  the  goods  to  which  it  related,  —  the  total 
consumption  of  all  borrowers  and  all  lenders  in  the 
country  considered. 

The  case  is  even  more  complicated,  however;  for  many 
borrowers  and  lenders  are  interested  less  in  consumption 
than  in  investment.^  The  choice  is  as  much  between 
lending  and  other  investing  as  between  lending  and  con- 
suming. Similarly,  the  borrower  may  borrow  to  invest 
as  well  as  to  consume  and  may  raise  the  money  for  repay- 
ment by  curtailing  investment  rather  than  by  curtailing 
consumption.     Borrowers  and  lenders,  in  other  words, 

*  Cf.  Kemmerer,  Quarterly  Journal  of  Economics,  August,  1909. 


214  THE    PURCHASING    POWER   OF   MONEY       [Chap.  X 

may  be  more  interested  in  purchasing  factories,  railroads, 
land,  durable  houses,  etc.,  which  yield  services  during 
a  long  future,  than  in  purchasing  more  or  better  food, 
shelter  and  entertainments,  which  yield  immediate 
satisfactions.  To  base  our  index  number  for^  time  con- 
tracts solely  on  services  and  immediately  consumable 
goods  would  therefore  be  illogical.  Though  the  prac- 
tical differences  may  amount  to  little,  yet,  in  theory  at 
least,  they  are  important. 

Let  us  suppose  each  price  ratio  to  be  weighted  by 
the  value  (at  standard  prices)  of  the  services  of  quickly 
consumable  goods  enjoyed  during  a  given  period,  pur- 
chases of  durable  capital  being  omitted.  Suppose  also 
that  before  the  time  of  repayment  arrives  the  rate 
of  interest  has  risen.  With  higher  interest,  the  value 
of  land,  railroads,  and  other  durable  capital  will  be  lower 
because  the  value  depends  on  future  earnings  or  future 
services,  and  these  are  now  discounted  at  a  higher  rate.^ 
The  borrower,  in  paying  back  an  equal  purchasing 
power  over  consumable  goods  and  services,  is  pay- 
ing back  a  much  higher  purchasing  power  over  such 
things  as  land,  houses,  and  factories  —  a  much  higher 
purchasing  power  over  future  income  —  than  he  bor- 
rowed. The  lender  is  receiving  back,  therefore,  a  larger 
purchasing  power  over  these  durable  items  of  capital 
than  he  loaned,  though  not  a  larger  purchasing  power 
(except  for  the  interest)  over  inmiediately  consumable 
goods  and  services.  He  gets  back  no  more  control  over 
present  income,  but  he  gets  a  purchasing  power  over 
a  greater  amount  of  deferred  income.     Had  he  invested 

^  For  a  discussion  of  the  effect  of  a  change  in  the  rate  of  interest 
on  prices,  see  Irving  Fisher,  Nature  of  Capital  and  Income,  New 
York  (Macmillan),  1906,  p.  227,  and  Rate  of  Interest,  New  York 
(Macmillan),  1907,  pp.  226  and  227. 


Sec.  3]  THE   BEST   INDEX   NUMBERS  215 

in  land  at  the  start,  instead  of  lending,  the  rise  of  interest 
would  have  left  him  with  the  same  amount  of  land,  but 
a  less  value.  As  it  is,  he  gets  back  a  purchasing  power 
over  a  greater  amount  and  the  same  value  of  land.  An 
accident  has  made  the  lender  better  off  than  he  ex- 
pected, and  better  off  than  he  would  have  been  had  he 
invested  instead  of  loaning. 

If,  on  the  other  hand,  the  rate  of  interest  should  fall, 
the  borrower  will  be  benefited,  and  the  lender  injured. 
The  value  of  land  and  of  any  other  property,  the  income 
of  which  extends  far  into  the  future,  would  rise  in 
comparison  with  the  value  of  food,  shelter,  and  so  on. 
The  value  of  a  house  is  the  discounted  value  of  its 
future  rent  or  service  in  affording  shelter.  The  rate 
of  interest  having  fallen,  the  value  of  the  house  will  be 
higher,  in  comparison  with  the  yearly  rental  value, 
than  before.  To  repay  the  same  amount  of  purchasing 
power  over  shelter  as  was  borrowed  is  to  repay  less  than 
the  same  amount  of  purchasing  power  over  houses. 
The  borrower  is  benefited  to  the  extent  that  he  has  to 
curtail  investments  to  repay,  since  he  repays  a  less 
investing  power  although  as  great  a  spending  power. 
He  need  not,  therefore,  curtail  his  investments  in  land 
and  machinery  quite  so  much  as  he  otherwise  would 
have  to  do.  The  lender,  on  the  other  hand,  is  in  the 
same  degree  injured.  If  he  wishes  to  invest  in  durable 
capital,  such  as  an  office  building,  a  mine,  or  shares  in 
a  railroad,  he  cannot  purchase  as  much  of  these  with 
the  returned  principal  as  he  could  have  purchased  with 
the  same  principal  at  the  time  of  the  loan.  Had  he 
foreseen  the  fall  in  interest,  he  might  have  refused  to 
make  the  loan  and  invested  instead.  He  would  then 
have  had,  in  place  of  interest  on  a  loan,  a  return  on  his 
investment  and  a  larger  amount  of  capital  on  which 


216  THE    PURCHASING   POWER   OF  MONEY       [Chap.  X 

to  realize  future  income.  The  effect  of  the  fall  in  in- 
terest would  then  have  been,  not  to  decrease  the  re- 
turns on  his  investment,  but  to  increase  the  capitalized 
vahie  of  the  investment. 

It  appears,  then,  that  while  an  index  number  based 
on  services  and  the  less  durable  commodities  may  be 
adapted  to  time  contracts  between  a  borrower  intend- 
ing to  indulge  in  immediate  consumption,  and  a  lender 
intending  to  postpone  consumption  until  the  repay- 
ment of  the  loan,  such  an  index  number  is  not  entirely 
suited  to  contracts  one  or  both  parties  to  which  are 
interested  in  more  permanent  investment. 

Instead,  therefore,  of  basing  our  index  number  on 
consumable  goods  and  services  enjoyed  during  a  period, 
we  ought  rather  to  base  it  partly  on  these  and  partly  on 
the  amount  of  durable  capital.  Each  borrower  and 
each  lender  may  wish  to  make  a  different  distribution 
in  time  of  his  income  stream.^  One  man,  that  he  may 
have  a  large  income  in  the  future,  wants  to  invest ; 
another,  that  he  may  enjoy  a  large  income  soon,  does 
not  want  to  invest.  One  lender  is, 'therefore,  interested 
in  getting  back  as  much  durable  capital  as  he  lent ; 
another  lender  is  interested  in  receiving  as  great  pur- 
chasing power  over  services  and  consumable  goods 
as  he  lent. 

Now  different  persons,  with  different  intentions  as 
to  the  spending  of  their  money,  nevertheless  make 
loan  contracts  with  each  other.  Even  if  a  separate 
index  number,  specially  weighted,  could  be  used  for 
each  couple,  such  a  standard  would  not  be  equally 
fitted  to  both  parties.  Yet  the  same  debt  cannot  be 
paid  in  two  different  standards.  Therefore,  absolute 
equalization  is  out  of  the  question.     We  can  mitigate 

1  Rate  of  Interest,  pp.  121-125. 


Sec.  4]  THE   BEST  INDEX  NUMBERS  217 

the  evils  of  a  fluctuating  money  standard,  but  we  cannot 
entirely  remove  the  element  of  speculation  from  time 
contracts. 

Although  different  persons  and  different  classes 
might  establish  different  standards  for  special  contracts, 
yet  for  the  great  mass  of  business  contracts  involving 
postponed  payments,  a  single  series  of  index  numbers 
including  articles  used  and  purchased  by  all  classes, 
and  including  also  services,  would  probably  be  found 
advisable.  This  index  number  would  be  best  suited 
to  contracts  between  different  classes,  between  in- 
dividuals of  differing  habits  of  consumption,  and  to  fix 
the  money  payments  on  bonds  which  are  securities 
sold  to  the  public  in  general. 

Without  attempting  to  construct  index  numbers 
which  particular  persons  and  classes  might  sometimes 
wish  to  take  as  standard,  we  shall  merely  inquire  re- 
garding the  formation  of  such  a  general  index  number. 
It  must,  as  has  been  pointed  out,  include  all  goods  and 
services.  But  in  what  proportion  shall  these  be 
weighted?  How  shall  we  decide  how  much  weight 
should  be  given,  in  forming  the  index,  to  the  stock  of 
durable  capital  and  how  much  weight  to  the  flow  of 
goods  and  services  through  a  period  of  time,  —  the  flow 
to  individuals,  which  mirrors  consumption?  The  two 
things  are  incommensurable.  Shall  we  count  the  rail- 
ways of  the  country  as  equally  important  with  a  month's 
consumption  of  sugar,  or  with  a  year's? 

§4 

To  cut  these  Gordian  knots,  perhaps  the  best  and 
most  practical  scheme  is  that  which  has  been  used  in 
the  explanation  of  the  P  in  our  equation  of  exchange, 
an  index  number  in    which    every  article  and  service 


218  THE    PURCHASING   POWER   OF  MONEY      [Chap.  X 

is  weighted  according  to  the  value  of  it  exchanged  at 
base  prices  in  the  year  whose  level  of  prices  it  is  desired 
to  find.^  By  this  means,  goods  bought  for  immediate 
consumption  are  included  in  the  weighting,  as  are  also 
all  durable  capital  goods  exchanged  during  the  period 
covered  by  the  index  number.  What  is  repaid  in  con- 
tracts so  measured  is  the  same  general  purchasing 
power.  This  includes  purchasing  power  over  every- 
thing purchased  and  purchasable,  including  real  estate, 
securities,  labor,  other  services,  such  as  the  services 
rendered  by  corporations,  and  commodities. 

There  has  been  much  discussion  as  to  the  propriety 
of  the  inclusion  of  services  of  human  beings,  or  so-called 
''labor."  In  one  way  the  question  solves  itself,  since 
the  inclusion  or  exclusion  on  the  basis  of  piece  work  will 
make  little  or  no  difference  to  the  results. 

It  is  well  known  that  we  may  measure  wages  either 
"  by  the  piece "  or  by  "time."  In  either  case  they  enter 
into  and  affect  the  general  index  number  expressing 
the  price  level,  but  the  influence  is  different  in  the 
two  cases.  If  we  take  hours  of  labor  as  the  basis  and 
measure  the  wages  paid  by  the  hour  or  by  the  day, 
then  we  are  likely  to  find  that,  during  a  period  of 
improvement  in  the  arts,  money  wages  are  rising  while 
the  prices  of  goods  are  falling,  or  that  money  wages  are 
rising  faster  than  the  prices  of  goods,  or  are  falling  more 
slowly.  But  if  we  measure  wages  by  the  piece,  we  shall 
find  less  inconsistency  of  results.  If  goods  increase 
faster  than  currency,  so  that  prices  tend  to  fall,  piece 

1  The  same  conclusion  as  to  the  best  standard  for  deferred  pay- 
ments is  reached  by  Professor  H.  S.  Foxwell  by  a  somewhat  differ- 
ent Hue  of  reasoning.  See  remarks  of  Professor  F.  Y.  Edgeworth 
(as  Secretary  of  the  Committee  on  Variations  of  the  Monetary 
Standard).  Report  of  the  British  Association  for  the  Advancement 
of  Science,  for  1889,  pp.  134-139. 


Sec.  4]  THE   BEST  INDEX  NUMBERS  219 

wages  will  tend  to  fall,  on  the  average,  in  very  much 
the  same  proportion.  As  improvements  in  machinery 
make  the  output  per  hour  of  labor,  i.e.  the  piece  work, 
increase,  the  price  per  piece  may  decrease. 

The  two  methods  of  measurement  giving  these  differ- 
ent results  for  price  indexes  make  opposite  differences 
in  the  volume  of  trade.  The  volume  of  piece  work 
increases  with  progress  in  invention  faster  than  the 
volume  of  time  work. 

In  considering  the  index  number  as  a  standard  for 
deferred  payments,  the  desirability  of  assuming  piece 
wages  to  change  like  commodity  prices  is  based  largely 
on  the  difficulty  and  consequent  impracticability  of 
including  wages  on  a  time  basis.  On  the  piece-wage 
basis,  changes  in  money  prices  of  other  goods  furnish 
an  approximate  measure  of  changes  in  money  prices 
of  labor. 

Those  who  make  time  contracts  on  the  basis  of 
such  an  index  number  know  that  they  will  pay  back, 
or  receive  back,  purchasing  power  over  the  same 
quantities  of  goods,  the  purchasing  power  over  which 
they  borrowed  or  lent.  This  form  of  index  number  is 
an  objective  standard  of  goods. 

If  an  index  number  were  to  be  constructed  from  time 
wages  alone  (not  including  goods  at  all),  debtors  would 
pay  back  and  creditors  receive  an  equivalent  purchas- 
ing power  over  hours  of  labor.  When  the  time  wages 
and  prices  of  goods  are  both  included,  the  problem  is 
how  much  weight  to  give  to  each.  Kemmerer  weights 
wages  3  per  cent  out  of  a  total  of  100  per  cent.  Its 
influence,  therefore,  would  in  any  case  not  be  felt 
greatly,  while,  if  we  take  piece  wages,  it  will  not  be  felt 
at  all;  that  is,  it  will  not  greatly  matter  whether 
wages  are  included  or  not.     Since  practically  we  have 


220  THE    PURCHASING   POWER   OF  MONEY       [Chap.  X 

no  statistics  of  relative  piece  wages,  and  few  good 
statistics  for  time  wages,  we  may,  in  general,  as  well 
omit  wages  altogether. 

This  procedure  has  another  advantage.  In  an  index 
number  intended  to  serve  as  a  basis  for  deferred  pay- 
ments for  wage  earners,  it  is  clear  that  wages  should 
be  excluded.  A  wage  earner  does  not  judge  his  pur- 
chasing power  on  the  basis  of  how  much  labor  he  can 
buy.^ 

In  this  connection  it  may  be  well  to  call  attention 
to  another  standard  of  purchasing  power  of  money 
which  has  sometimes  been  suggested  for  adjusting 
contracts.  This  is  the  utility  standard.  According 
to  this,  each  person  would  be  expected  to  receive  or 
pay  back  marginal  utility  equivalent  to  what  he  had 
lent  or  borrovred.  But  the  marginal  utility  of  the 
same  goods  is  different  for  different  persons  and  different 
for  the  same  person  at  different  periods  of  his  life. 
Hence,  no  such  standard  could  be  practically  applied. 

A  price  is  an  objective  datum,  susceptible  of  measure- 
ment, and  the  same  for  all  men.  Marginal  utilities, 
on  the  other  hand,  not  only  are  impossible  to  meas- 
ure, but  are  unequal  and  vary  unequally  among  in- 
dividuals. The  purchasing  power  of  money  in  the 
objective  sense  is,  therefore,  an  ascertainable  magnitude 
with  a  meaning  common  to  all  men.  It  is  of  course  true 
that  marginal  utility  of  money  is  a  fundamental  magni- 
tude and  that  it  depends  in  part  on  the  purchasing 
power  of  money.  But  it  depends  also  on  each  man's 
income.  The  marginal  utilities  of  money  will  vary 
directly  with  the  purchasing  power  of  money  if  aU 
prices  and  all  money  incomes  change  in  the  same  ratio,  or 

1  Cf.  Edgeworth,  in  Palgrave's  Dictionary  of  Political  Economy^ 
"Index  Numbers." 


Sec.  4]  THE   BEST   INDEX   NUMBERS  221 

(roughly  at  least)  if  incomes  change  in  the  ratio  of  the 
average  price  change.  Ideally,  this  fixed  ratio  between 
marginal  utilities  and  purchasing  power  should  hold 
true  when  the  quantity  of  money  varies  (assuming  that 
deposits  vary  equally  and  that  velocities  of  circulation 
and  volume  of  trade  remain  unchanged)  after  transi- 
tion periods  are  over.  Practically,  however,  all  these 
elements  vary,  and  vary  unequally.  Money  incomes 
sometimes  increase  faster,  often  more  slowly,  than 
prices.  The  result  is  that  changes  in  the  purchasing 
power  of  money  do  not  correspond  to  changes  in  mar- 
ginal utilities  of  money. 

Society  may  become  more  prosperous,  or  it  may  be- 
come less  so,  during  the  time  a  contract  has  to  run. 
This  fact,  it  may  be  thought,  should  influence  the  re- 
lation of  the  amount  repaid  to  the  amount  borrowed. 
It  has  been  claimed  that  the  benefits  of  progress 
should  be  equably  distributed  between  borrowers  and 
lenders.^ 

But  while  loan  contracts  are  made  with  reference  to 
marginal  utilities,  it  is  here  contended  that  corrections 
in  a  monetary  standard  not  only  cannot,  but  should  not, 
include  variations  in  the  subjective  value  of  money 
due  to  changes  in  incomes,  but  should  be  confined  to 
variations  in  objective  purchasing  power.  At  any  rate, 
to  obtain  a  measure  of  objective  purchasing  power  is 

^  See,  for  example,  paper  by  Professor  J.  B.  Clark,  "The  Gold 
Standard  in  Recent  Theory,"  Political  Science  Quarterly,  Septem- 
ber, 1895.  Compare  with  this  "The  Standard  of  Deferred  Pay- 
ments," by  Professor  Edward  A.  Ross,  Annals  of  the  American 
Academy  of  Political  and  Social  Science,  November,  1892  ;  Lucius  S. 
Merriam,  "  The  Theory  of  Final  Utility  in  its  Relation  to  Money 
and  the  Standard  of  Deferred  Payments,"  ibid.,  January,  1893  ;  Pro- 
fessor Frank  Fetter,  "  The  Exploitation  of  Theories  of  Value  in  the 
Discussion  of  the  Standard  of  Deferred  Payments,"  ibid.,  May,  1895. 


222  THE   PURCHASING   POWER   OF  MONEY      [Chap.  X 

a  step  which  may  properly  be  taken  by  itself  before 
any  step  more  ambitious  is  considered.  The  search  for 
a  standard  of  deferred  payments  which  shall  auto- 
matically provide  for  the  just  distribution  of  the  "  ben- 
efits of  progress  "  seems  as  fatuous  a  quest  as  the  search 
for  the  philosopher's  stone.  Since  we  cannot  measure 
utility  statistically,  we  cannot  measure  the  corrections 
in  utility  required  to  redistribute  the  "  benefits  of  prog- 
ress." In  the  absence  of  statistical  measurement,  any 
practicable  correction  is  out  of  the  question.  The 
''utility  standard"  is  therefore  impracticable,  even  if 
the  theory  of  such  a  standard  were  tenable. 

Somewhat  similar  theories  of  a  perfect  standard  of 
deferred  payments  are  based  on  the  idea  that  a  dollar 
should  require  always  the  same  amount  of  labor  to  pro- 
duce it.  In  one  sense,  since  marginal  utility  and  mar- 
ginal effort  are  normally  equal,  the  labor  standard  is 
identical  with  the  marginal  utility  standard.  But  in 
whatever  sense  ''labor"  is  defined,  it  is  an  elusive  mag- 
nitude, quite  impracticable  as  a  measurable  basis  for 
statistics  of  purchasing  power.  Seemingly  labor  may 
be  measured  in  terms  of  time  and,  on  such  a  basis,  "  a 
day's  labor "  has  been  suggested  as  a  proper  unit  for 
measuring  deferred  payments.  But  even  "  a  day's 
labor"  is  not  a  sufficiently  definite  unit  in  which  to 
measure  with  any  considerable  degree  of  accuracy  the 
purchasing  power  of  money.  Days'  labor  differ  in 
hours,  in  intensity,  and  disagreeability  of  effort  as  well 
as  in  the  quality  of  labor  performed  —  whether  it  be 
manual,  mental,  etc.  A  magnitude  which  offers  so 
many  theoretical  difficulties  in  measurement  can  never 
serve  as  a  practical  standard  of  deferred  payments. 

We  see  then  that  the  attempt  to  set  up  a  utility 
or  labor  standard  is  too  ambitious  to   be  practica- 


Sec.  4]  THE   BEST  INDEX   NUMBERS  223 

ble.^  We  should  content  ourselves  with  securing  the 
maximum  attainable  improvement  in  the  standard  of 
deferred  payments,  without  attempting  to  secure  an 
ideal  distribution  of  "  the  benefits  of  progress." 

It  will  also  simplify  our  problem  if  we  remember  that 
our  ideal  is  not  primarily  constancy  of  •  the  dollar  but 
rather  dependability.  Fluctuations  which  can  be  fore- 
seen and  allowed  for  are  not  evils.  Each  man  may 
presumably  be  depended  on  to  allow  for  changes  in  his 
own  fortunes,  utility,  and  labor,  and  perhaps  even  to  a 
large  extent  on  the  general  effects  of  invention  and  prog- 
ress. At  any  rate  he  should  not  expect  the  monetary 
unit  to  insure  him  against  every  wind  that  blows. 

The  manner  in  which  each  person  allows  for  such 
future  changes  as  he  can  foresee  is  by  adjusting  the 
size  of  loans  he  makes  or  takes  and  the  rate  of  interest 
thereon.  If  the  average  income  is  rising,  the  borrower 
can  afford  to  repay  more  and  the  lender  should  receive 
more ;  while,  if  the  average  income  is  falling,  the 
amount  paid  should  be  less.  The  fact  is  that  such  are 
the  tendencies  where  the  rise  or  fall  of  average  income 
is  foreseen.  If  the  average  income  is  rising,  the  lender 
will  be  less  anxious  to  deplete  his  present  income,  which 
is  relatively  meager,  in  order  to  increase  his  future  in- 
come, which  he  sees  will  probably  be  larger  anyway. 
Thus,  increasing  prosperity  (by  which  is  meant,  not 
great  prosperity,  but  growing  prosperity)  tends  to  re- 
strict the  supply  of  loans.  At  the  same  time,  it  tends  to 
increase  the  demand  and  so  raise  interest.  Conversely, 
a  decreasing  average  income  will  tend  to  lower  interest.^ 

*  Cf.  Charles  A.  Conant,  The  Principles  of  Money  and  Banking, 
Vol.  II,  Chapter  VII. 

^  Rate  of  Interest,  pp.  95-98  and  304-306.  This  position  is  taken 
by  Correa  Moylan  Walsh,  The  Fundamental  Problem  in  Monetary 
Science,  New  York  (Macmillan),  1903,  p.  345,  footnote. 


224  THE    PURCHASING   POWER   OF  MONEY       [Chap.  X 

All  this  follows  only  in  case  the  rise  or  fall  of  incomes 
is  foreseen.  If  not  foreseen,  it  can  exercise  no  influence 
of  importance  on  the  interest  rate.  To  the  extent 
that  such  changes  come  unexpectedly  after  loan  con- 
tracts have  been  entered  into  which  take  no  account 
of  them,  —  to  that  extent  loan  contracts  are  speculative. 
If  incomes  fall,  the  lender  has  gained  relatively  to  the 
borrower,  because  he  has  realized  a  higher  interest  than 
he  could  have  realized  had  the  change  been  foreseen. 
The  chief  burden  of  the  change  falls  on  the  borrower. 
If  incomes  experience  an  unexpected  rise,  the  relative 
positions  are  reversed ;  the  whole  gain  goes  to  the 
borrower.  The  normal  effect  of  continuous  extension 
of  income  is  to  raise  the  rate  of  interest. 

Our  present  problem,  however,  is  not  to  safeguard 
the  interests  of  debtors  and  creditors  against  all  pos- 
sible elements  of  change,  but  only  against  those  ele- 
ments which  are  purely  monetary.  Industrial  changes 
are  in  a  class  by  themselves,  and  contracting  parties 
must  be  trusted  to  work  out  their  own  salvation.  We 
are  merely  concerned  in  providing  them  with  a  stable 
or  reliable  monetary  standard.  A  secure  monetary 
standard  cannot  guarantee  against  earthquake  nor  in- 
sure the  equable  distribution  of  prosperity.  It  can, 
however,  mitigate  the  losses  now  suffered  from  changes 
in  the  relation  of  money  to  other  goods. 

Statistics  of  nominal  or  money  interest  rates  and 
virtual  or  commodity  interest  rates  prove  that  the 
latter  fluctuate  much  more  than  the  former.^  The 
effects  of  this  lack  of  compensation  are  evil.  In  the 
first  place,  the  situation  interferes  with  the  normal  dis- 
tribution of  wealth  and  income.  If  the  level  of  prices 
is  rising,  since  nominal  interest  does  not  for  a  con- 

1  Rate  of  Interest,  Chapter  XIV. 


Sec.  5]  THE   BEST   INDEX  NUMBERS  225 

siderable  time  rise  enough  to  compensate,  the  lender 
gets  back  a  less  amount  of  wealth  or  services  than  he 
might  reasonably  have  expected.  Creditors  lose  and 
debtors  gain.  It  should  be  noted  also  that  all  persons 
with  relatively  fixed  money  salaries  lose  by  this  rise 
of  prices.  When  the  level  of  prices  falls,  on  the  other 
hand,  creditors  and  persons  with  relatively  fixed  in- 
comes gain  at  the  expense  of  debtors.  The  distribu- 
tion of  wealth  is  changed  in  either  case  from  purely 
monetary  causes,  and  the  change  can  be  averted  by 
making  the  standard  of  deferred  payments  more  stable. 

§5 

We  are  brought  back  again,  therefore,  to  the  conclusion 
that  on  the  whole  the  best  index  number  for  the  purpose 
of  a  standard  of  deferred  payments  in  business  is  the 
same  index  number  which  we  found  the  best  to  indicate 
the  changes  in  prices  of  all  business  done ;  —  in  other 
words,  it  is  the  P  on  the  right  side  of  the  equation  of 
exchange.^ 

It  is,  of  course,  utterly  impossible  to  secure  data  for 
all  exchanges,  nor  would  this  be  advisable.  Only 
articles  which  are  standardized,  and  only  those  the  use 
of  which  remains  through  many  years,  are  available 
and  important  enough  to  include.  These  specifica- 
tions exclude  real  estate,  and  to  some  extent  wages, 
retail  prices,  and  securities,  thus  leaving  practically 
nothing  but  wholesale  prices  of  commodities  to  be  in- 
cluded in  the  list  of  goods,  the  prices  of  which  are  to  be 

1  This  is  really  the  same  conclusion  as  that  reached  by  Walsh, 
The  Fundamental  Problem  in  Monetary  Science,  in  which,  after  a 
thorough  and  critical  review  of  the  literature  of  the  subject,  the 
author  concludes  that  the  kind  of  stability  desirable  in  the  standard 
of  deferred  payment  is  "stability  of  exchange  value.'' 
Q 


226  THE    PURCHASING   POWER   OF  MONEY      [Chap.  X 

compounded  into  an  index  number.  These  restrictions, 
however,  are  not  as  important  as  might  be  supposed. 
The  total  real  estate  transactions  of  New  York  City 
(Manhattan  and  the  Bronx)  in  1909  (an  active  year) 
measured  by  assessed  valuations  (probably  |  of  the 
market  valuation)  amounted  to  only  $620,000,000. 
This  is  utterly  insignificant  if  compared  only  with  the 
104  billions  of  bank  clearings  in  New  York  City.  Yet 
real  estate  transactions  probably  constitute  a  higher 
percentage  of  total  transactions  in  New  York  than  in 
the  United  States.^  In  the  United  States  we  feel  safe, 
therefore,  in  saying  that  they  amount  only  to  a  fraction 
of  1  per  cent  of  the  total  transactions.  As  to  exchanges 
in  securities,  Kemmerer  estimates,  on  the  basis  of  the 
transactions  of  the  New  York  Stock  Exchange,  that 
about  8  per  cent  of  the  total  transactions  of  the  coun- 
try consist  in  the  transfer  of  securities.^  As  already 
stated,  he  also  estimates  that  wages  amount  to  about 
3  per  cent.^  As  to  the  comparative  importance  of 
retail  as  compared  with  wholesale  prices,  we  have 
some  figures  of  Professor  Eanley,  of  the  Monetary 
Commission.^  On  this  basis,  and  because  wholesale 
and  retail  prices   roughly   correspond  in   their  move- 

^  At  any  rate  the  impression  is  strong  that  real  estate  is  more 
"active"  in  New  York  than  in  most  other  cities,  because  of  the 
rapid  change  in  the  character  of  sites  on  account  of  the  narrowness 
of  Manhattan  Island  and  the  consequent  acceleration  of  growth 
in  one  direction  (northward)  and  that,  in  general,  cities  have  more 
trade  in  real  estate  than  the  country,  not  only  absolutely,  but  rela- 
lively  to  other  trade. 

*  Money  and  Prices,  2d  ed..  New  York  (Holt),  1909,  p.  138. 
« Ibid.,  p.  138. 

*  Credit  Instruments,  1910,  61st  Congress,  2d  Session,  Senate  Docu- 
ment 399,  pp.  69,  73,  134,  136,  would  indicate  that  wholesale  trade 
requires  something  like  twice  as  much  exchange  work  as  retail 
trade. 


Sec.  5]  THE   BEST  INDEX  NUMBERS  227 

ments,^  we  may  omit  retail  prices  altogether.  It  is  true 
that  retail  prices  usually  lag  behind  wholesale  prices ;  but 
part  of  the  lagging  is  more  apparent  than  real.  Expert 
testimony  of  those  who  have  collected  such  statistics 
shows  that  when,  as  at  present,  prices  are  rising  rapidly, 
retailers  obviate  the  necessity  of  confronting  their 
customers  with  too  frequent  and  rapid  increases  in 
prices  by  quoting  the  same  prices  and  substituting  in- 
ferior grades  or,  in  some  instances,  smaller  loaves  or 
packages. 

It  is  true  that  wholesale  transactions  constitute 
a  minority  of  all  transactions,  perhaps  only  a  fifth. ^ 
Nevertheless,  wholesale  prices  are  more  typical  than 
any  other. 

They  are  to  a  large  extent  typical  of  producers' 
prices  which  precede  them,  and  of  retail  prices  which 
succeed  them.  They  are  typical  of  many  large  and 
often  nondescript  groups  which  go  to  make  up  the  total 
transactions,  such  as  are  classed  together  in  Kinley's 
Report  to  the  Monetary  Commission  under  the  head 
''other  deposits,"  including  hotel  charges,  fees  of  pro- 
fessional men,  etc.,  as  well  as  wages.  Among  items  of 
which  wholesale  prices  may  not  be  very  typical  are 
the  transactions  in  securities  (speculative  and  other), 
railway  and  other  transportation  charges,  and  insurance. 
Latterly,  prices  of  stock  securities  have  advanced  faster 
than  wholesale  prices,  while  transportation  and  insur- 
ance charges  have  not  advanced  as  fast.    The  attempts 

1  The  studies  of  the  Bureau  of  Labor  in  retail  prices  seem  to  show 
a  general  sympathy  in  movement  between  retail  or  wholesale  prices, 
as  indeed  might  be  expected. 

2  See,  in  Report  of  National  Monetary  Comviission  on  Credit 
Instruments,  the  figures  of  aggregate  sums  deposited  in  banks  by 
wholesale  merchants  and  others.  While  these  do  not  afford  an  ex- 
act comparison,  they  aid  in  making  a  rough  guess. 


228  THE    PURCHASING   POWER  OF  MONEY       [Chap.  X 

of  Kemmerer  and  myself  (Chapter  XII)  to  combine  in 
one  average  wholesale  prices  and  prices  of  stocks  and 
wages  yield  results  differing  only  slightly  from  those 
based  on  wholesale  prices.  From  a  practical  stand- 
point, wholesale  prices  of  commodities  are  the  only 
prices  which  are  yet  sufficiently  standardized,  and  the 
use  of  the  goods  sufficiently  stable  through  a  long 
period  of  time,  to  make  them  serviceable  for  general 
use. 

Not  only  may  we  consider  that  wholesale  prices 
roughly  represent  all  prices,  but  we  may,  with  even  more 
confidence,  confine  our  statistics  for  wholesale  prices 
to  a  relatively  small  number.  Edgeworth  and  others 
have  shown,  both  practically  and  theoretically,  that 
a  large  number  of  articles  is  needless  and  may  even 
be  detrimental.  The  22  commodities  employed  by 
''The  Economist"  afford  an  index  number  of  con- 
siderable value;  the  45  of  Sauerbeck  have  given  us  a 
standard  of  great  value;  and  the  200  and  more  com- 
modities used  in  the  Aldrich  Report  and  the  bulle- 
tins of  the  Bureau  of  Labor  are  certainly  numerous 
enough,  if  not  too  numerous,  to  give  a  most  accurate 
index  number  of  prices. 

The  recommendations  of  the  Committee  of  the 
British  Association  for  the  Advancement  of  Science 
were  that  the  index  number  should  include  six  groups, 
comprehending  twenty-seven  classes  of  articles,  and 
that  the  prices  should  be  weighted  in  round  numbers 
representing  approximately  the  relative  expenditures 
of  the  community  in  these  objects.  The  groups  and 
classes  with  weighting  were  as  follows :  ^  — 

^  See  Report  of  the  Committee  in  Report  of  the  British  Associa- 
tion for  the  Advancement  of  Science,  for  1888,  p.  186. 


Sec.  5]  THE   BEST   INDEX   NUMBERS  229 

Breadstuffs  (wheat  5,  barley  5,  oats  5,  potatoes,  rice,  etc.,  5)    .     .  20 

Meat  and  dairy  (meat  10,  fish  21,  cheese,  butter,  milk,  71)  ...  20 
Luxuries  (sugar  2i,  tea  2z,  beer  9,  spirits  2i,  wine  1,  tobacco 

2i) 20 

Clothing  (cotton  2i,  wool  2i,  silk  2i,  leather  2i) 10 

Minerals  (coal  10,  iron  5,  copper  2j,  lead,  zinc,  tin,  etc.,  2^)  .  .  20 
Miscellaneous  (timber  3,  petroleum  1,  indigo  1,  flax  and  linseed 

3,  palm  oil  1,  caoutchouc  1) 10 

This  report  was  made  after  very  thorough  considera- 
tion by  a  remarkably  competent  committee  consisting 
of  Mr.  S.  Bourne,  Professor  F.  Y.  Edgeworth  (Sec), 
Professor  H.  S.  Foxwell,  Mr.  Robert  Giffen,  Professor 
Alfred  Marshall,  Mr.  J.  B.  Martin,  Professor  J.  S. 
Nicholson,  Mr,  R.  H.  Inglis  Palgrave,  and  Professor 
H.  Sedgwick.  The  report  also  gives  the  precise  techni- 
cal description  of  the  articles  the  price  quotations  of 
which  are  to  be  used  (the  iron,  for  instance,  being 
''Scotch  pig  iron"),  and  also  the  price  list  or  other  source 
for  price  quotations  (the  wheat,  for  instance,  being  the 
''Gazette  Average"). 

With  slight  modifications  this  recommendation  of 
the  British  Committee  could  be  made  to  apply  to 
American  figures.  In  America  we  have  had  a  number 
of  index  numbers  of  wholesale  prices,  the  most  im- 
portant being  (1)  those  of  Roland  P.  Falkner  in  the 
Aldrich  Senate  Report,  covering  a  period  from  1840 
to  1891,  in  which,  beginning  with  1860,  there  were  223 
commodities  included,  the  results  being  given  in  two 
ways,  viz.,  weighted,  the  weighting  being  arranged  accord- 
ing to  relative  expenditures  on  these  articles  or  their 
congeners  used  by  workmen,  and  also  unweighted ; 
(2)  those  of  the  United  States  Labor  Bureau  for  251  to 
261  commodities  beginning  with  1890,  and  now,  it  is 
understood,  to  be  published  every  year;    (3)   Dun's 


230  THE    PUKCHASING   POWER  OF  MuNEY      [Chap.  X 

index  numbers  from  1860  to  1906  continued  recently 
for  Gibson  by  Dr.  J.  P.  Norton ;  and  (4)  Bradstreet's 
index  numbers  since  1895  for  96  commodities. 

We  need  not  go  into  detailed  criticism  of  these  index 
numbers.  On  the  whole  they  seem  to  include  too  many 
commodities,  while  they  all  employ  the  objectionable 
fixed-base  system.  It  would  be  a  great  advantage  if  we 
could  fix  upon  a  system  in  America  which  would  be  not 
only  authoritative,  but  would  give  out  its  results  at 
least  yearly  and  promptly. 

For  practical  purposes  the  median  is  one  of  the  best 
index  numbers.  It  may  be  computed  in  a  small  fraction 
of  the  time  required  for  computing  the  more  theoret- 
ically accurate  index  numbers,  and  it  meets  many  of 
the  tests  of  a  good  index  number  remarkably  well. 
It  also  has  the  advantage  of  easily  exhibiting  (by  means 
of  the  ''quartiles")  the  tendency  to  dispersion  of  prices 
(from  each  year  as  a  base  to  the  next)  on  either  side 
of  the  median.  The  median  should  be  weighted  in 
round  numbers  analogously  to  the  weighting  already  dis- 
cussed for  the  more  theoretically  perfect  index  numbers.^ 
The  median  of  a  series  of  numbers  is  a  number  such 
that  there  are  as  many  numbers  above  as  below  it  in 
the  series.  If  the  number  of  terms  in  the  series  is  odd, 
the  median  is  the  middle  term  of  the  series  of  numbers 
arranged  in  the  order  of  magnitude.  If  the  number  of 
terms  is  even,  the  median  falls  between  two  terms.  If 
these  are  equal,  the  median  is  identical  with  them  both; 
if  they  are  unequal,  the  median  lies  between  them  and 
may  then  be  taken  as  their  simple  arithmetical,  geo- 
metric, or  any  other  average.  Practically  the  two 
middle  terms  are  almost  inevitably  so  close  together 
that  it  would  make  no  appreciable  difference  what 
\See  Appendix  to  (this)  Chapter  X,  §  8. 


Sec.  6]  THE    BEST   INDEX  NUMBERS  231 

method  of  averaging  the  two  middle  terms  is  adopted. 
The  method  of  weighting  the  terms  from  which  a 
median  is  computed  consists  in  counting  each  term  the 
number  of  times  indicated  by  its  weight.  To  illustrate 
these  statements,  it  is  evident  that  the  median  of  the 
numbers  3,  4,  4,  5,  6,  6,  7,  arranged  in  order  of  magni- 
tude is  5 ;  and  the  median  of  3,  4,  4,  5,  6,  6  is  4^. 
If  the  weights  to  be  attached  to  these  latter  numbers  are 

for  number  3  weight  1 
for  number  4  weight  2 
for  number  4  weight  3 
for  number  5  weight  4 
for  number  6  weight  2 
for  number  6  weight  1 

the  median  is  then  found  from  the  following :  — 

Series 3,  4,  4,  4,  4,  4,  5,  5,  5,  5,  6,  6,  6 

The  weights  being 12  3  4  2    1 

of  which  the  median  is  5.  The  arithmetical  averages 
corresponding  to  the  three  medians  mentioned  (5,  4J 
and  5)  are  5.,  4.67  and  4.69  respectively. 

Practically  it  is  not  necessary  to  arrange  the  terms 
in  exact  order  of  size.  Terms  easily  recognized  as  low 
can  readily  be  paired  off  against  those  easily  recognized 
as  high  and  only  the  remaining  few  central  terms  need 
be  arranged  in  exact  order.  The  terms  near  the  middle 
being  usually  almost  or  quite  equal,  make  the  selection 
of  the  median  extremely  easy. 

In  order  to  use  the  median  for  an  index  number  of 
prices,  we  first  arrange  our  yrice  ratios  and  then  select 
the  median  ratio. 

§  6 

In  this  chapter  we  have  aimed  to  show  that  an  excel- 
lent form  of  index  number  of  prices  is  the  ratio  of  real 


232  THE   PURCHASING   POWER   OF  MONEY       [Chap.  X 

values  to  ideal  values  at  base  prices ;  and  that  the  ele- 
ments entering  into  the  construction  of  index  numbers 
differ  according  to  the  different  purposes  for  which  they 
are  desired.  If  the  purpose  is  to  measure  capital,  the 
prices  of  services  should  not  be  included,  but  only  the 
prices  of  the  different  articles  of  wealth  existing  at  any 
point  of  time.  If  the  purpose  is  to  obtain  means  to 
measure  real  wages,  only  those  things  should  be  in- 
cluded which  workingmen  buy ;  and  they  should  be 
included  according  to  the  values  bought  during  a  given 
period,  these  values  being  measm-ed  at  standard  prices. 

The  question  of  justice  between  borrower  and  lender, 
where  the  purpose  is  to  fix  on  the  best  index  number  as 
a  standard  for  deferred  payments,  was  also  considered. 
It  was  seen  to  be  not  an  infringement  of  justice  that  one 
man  should  gain  from  another  on  account  of  fluctuations 
in  the  money  standard ;  for  the  contract  is  a  free  one 
in  which  normally  each  should  assume  whatever  risk 
there  may  be  of  loss  for  the  sake  of  whatever  chance 
there  may  be  of  gain.  It  was  maintained,  also,  that 
it  would  be  wrong  for  the  government  deliberately  to 
take  his  gain  away  from  a  person  who  had  assumed  a 
risk  of  loss  in  the  first  place.  Nevertheless,  it  was  urged 
that  a  means  by  which  contracts  made  in  the  future 
could  be  made  less  speculative,  is  desirable. 

It  was  urged  that  it  is  no  part  of  the  function  of  an 
index  number  of  general  prices  to  guard  against  rising 
and  falling  real  income.  The  function  of  such  an  index 
number  is  to  measure  the  change  in  the  level  of  prices, 
in  order  that,  in  contracts  involving  deferred  payments, 
there  shall  be  no  element  of  risk  so  far  as  money  is  con- 
cerned. Without  the  index  number  as  a  standard,  such 
contracts  are  quite  highly  speculative.  The  adjustment 
of  the  rate  of  interest  compensates  to  some  extent,  but 


Sec.  6]  THE    BEST   INDEX   NUMBERS  233 

not  nearly  enough,  for  the  fluctuations  in  the  value  of 
money.  These  fluctuations  influence  the  distribution 
of  wealth  among  persons  and  classes,  and  bring  about 
crises  and  business  depressions.  It  is  desirable  that 
some  basis  for  time  contracts  should  be  fixed  upon, 
which  will  remedy  these  evils.  It  is  believed  that  an 
index  number  expressing  the  price  level  entering  into 
the  equation  of  exchange  might  be  adopted  as  such 
a  basis.  The  ideal  set  forth  is  that  neither  debtor 
nor  creditor  should  be  the  worse  off  by  being  deceived 
through  changes  in  the  level  of  prices  of  goods  bought 
and  sold.  Some  system  is  to  be  sought,  therefore,  by 
which  the  actual  results  of  the  contract  should  closely 
approximate  the  expected  results  in  nearly  all  cases. 

It  was  shown  that  different  persons  and  dift'erent 
classes  might  be  interested  in  having  for  their  time  con- 
tracts index  numbers  somewhat  differently  constructed, 
because  different  persons  are  interested  in  consuming 
different  kinds  of  commodities  and  because  they  desire 
to  invest  larger  or  smaller  proportions  of  their  earnings. 
But  for  general  purposes,  as  the  best  compromise  to 
fit  the  needs  of  different  classes,  what  was  suggested 
was  an  index  number  based  on  the  prices  of  all  goods 
exchanged  during  a  given  period.  It  was  pointed  out, 
however,  that  the  different  forms  of  index  numbers 
which  had  gained  reputation  lead  to  practically  the 
same  results. 

Finally,  it  was  shown  that  for  rough  and  ready  com- 
putations the  median  has  advantages  over  all  other 
forms  of  index  numbers. 


CHAPTER  XI 

STATISTICAL    VERIFICATION.      GENERAL    HISTORICAL 

REVIEW 

§    1 

Since  both  the  level  of  prices  and  the  quantity  of 
money  in  circulation  cannot  in  practice  be  perfectly 
measured,  and  since  the  level  of  prices  depends  upon 
other  factors  besides  the  quantity  of  money,  —  viz. 
the  quantity  of  circulating  credit,  the  velocities  of  cir- 
culation of  that  credit  and  of  money,  and  the  volume  of 
business,  —  it  would  be  absurd  to  expect  any  exact 
correspondence  between  variations  in  the  quantity  of 
circulating  money  and  variations  in  the  price  level ; 
and  it  is  likewise  absurd  to  state,  as  some  have  stated, 

that   the  absence  of   exact  statistical   correspondence 

* 

proves  the  absence  of  any  influence  of  quantity  of  money 
on  price  level.  Nevertheless,  when  the  volume  of  money 
changes  greatly  and  quickly,  the  effect  on  prices  from 
this  cause  is  usually  so  great  as  to  make  itself  manifest. 
The  general  trend  of  prices  has  usually  been  upward, 
as  Figure  10  ^  shows.  According  to  the  diagram  prices 
are  now  about  five  times  as  high  as  a  thousand  years 
ago  and  are  from  two  to  three  times  as  high  as  in  the 
period  between  1200  and  1500  a.d.'  Beginning  with 
the  last-named  date,  or  shortly  after  the  discovery  of 
America,  prices  have  almost  steadily  risen. 

1  This  diagram  shows  the  changes  in  price  level  according  to  the 
separate  estimates  of  D'Avenel,  Hanauer,  and  Leber  as  given  in 
Aupetit's  Essai  sur  la  theorie  generale  de  la  Tnonnaie,  Paris  (Gnillau- 
min),  1901,  p.  245. 

2  These  figures  are  found  by  supplementing  those  of  D'Avenel, 
Hanauer,  and  Leber  by  those  of  Jevons  and  Sauerbeck  in  the 
19th  century.  Without  such  supplementing  the  rise  is  still  more, 
being  tenfold  in  a  thousand  years  and  four  to  six  times  since 
1200-1500. 

234 


Sec.  1] 


STATISTICAL   VERIFICATION 


235 


The  discovery  of  America  was  followed  in  1519  by 
the  invasion  of  Mexico  under  Cortez  and,  twenty  years 
later,  by  Pizarro's  conquest  of  Peru.  From  these 
conquests  and  the  consequent  development  of  New 
World  mining  of  precious  metals,  dates  the  tremendous 
production  of  gold,  and  especially  of  silver,  during  the 
sixteenth  century.  From  the  discovery  of  America 
until  the  after  effects  of  its  discovery  began  to  be  felt, 


.. 

160 

•40 

»so 

t 

f 

\ 

/ 

1 

1 

\/ 

\, 

\, 

/ 

} 

\ 

HANAUER 

LEBER. 

1 

/ 

\ 

i 

s\ 

'  1 

\ 

1/ 

\ 

Z' 

\ 

I 

\ 

/ 

— ' 

/ 

\ 

A 

1 

\ 

1 

1 

^ 

— 

\ 

/ 

\ 

I 

\ 

1 

40 

_ 

— 

— 

/ 

_ 

— 

Sv, 

V 

-^ 

4 

/ 

L 

_ 

— 



— 

_ 



— 

~ 

— 

— 

— 

— 

— 

— 

— 

^ 

— 

— 

— 

— 

— 

— 

— 

- 

- 

— 

*" 

o 

650  /eOO  1300  lAOO  1300.  l&iO  1700  1800  1900 

Fig.  10. 


or,  to  be  exact,  through  the  year  1544,  the  average 
annual  output  of  gold  was  less  than  five  million  dollars, 
and  of  silver  about  the  same.^     The  rich  mines  of  Potosi 

1  These  and  the  following  figures  are  from  "The  World's  Pro- 
duction of  Gold  and  Silver  from  1493-1905,"  J.  D.  Magee,  Journal 
of  Political  Economy,  January,  1910,  p.  50  ff.  Mr.  Magee's  figures 
to  1885  are  based  on  Soetbeer's,  and  since  that  date,  on  the  Reports 
of  the  Director  of  the  United  States  Mint.  For  Soetbeer's  figures, 
see  Adolf  Soetbeer,  Edelmetall-Produklion  und  Werthverhdltniss 
zunschen  Gold  und  Silber  seit  der  Entdcckung  Amerika's  bis  zur 
Gegenwart,  Cotha  (Justus  Perthes),  1879,  p.  107.  These  figures 
and  others  to  follow  are  given  also  in  the  same  author's  Materialien 
and  are  quoted,  and  their  significance  discussed,  in  L.  L.  Price, 


236  THE    PURCHASING    POWER  OF  MONEY       [Chap.  XI 

in  Bolivia  were  discovered  in  1546.  From  1545  to  1560 
the  annual  production  of  silver  averaged  eighteen  mil- 
Uons,  which  was  over  fourfold  the  previous  rate.  The 
product  of  gold  also  increased,  though  slightly.  The 
rates  of  production  for  both  metals  rose  steadily  (with 
slight  interruption,  1811-1840)  up  to  the  present  time. 

These  new  world  mines  began  to  pour  their  product 
into  Europe :  first  into  Spain,  the  chief  owner  of  the 
mines,  then,  by  trade,  into  the  Netherlands  and  other 
parts  of  Europe,  and  then  into  the  Orient  —  that  great 
''sink  of  silver."  Accordingly,  as  Cliff e  Leslie^  has 
shown,  prices  rose  first  in  Spain,  then  in  the  Nether- 
lands, and  then  in  other  regions. 

But,  though  the  new  supphes  of  the  precious  metals 
distributed  themselves  very  gradually  through  Europe, 
and  the  rise  of  prices  was  consequently  in  some  regions 
delayed,  there  can  be  no  doubt  that  they  rose  or  that 
the  rise  was  great.  The  rise  between  the  discovery  of 
America  and  the  beginning  of  the  nineteenth  century 
was  several  hundred  per  cent.  This  rise  was  simul- 
taneous with  an  increase  of  the  stock  of  the  precious 
metals,  because  production  outran  consumption. 

Although  the  total  production  of  the  precious  metals 
continued  to  increase  until  1810,  the  ratio  of  the  yearly 
production  to  the  existing  stock  became  gradually  less. 
Corresponding  to  this  slackening  of  production,  and 
presumably  because  of  it,  prices  did  not  continue  to  rise 
at  the  same  rapid  rate  as  at  first.  Furthermore,  with 
the  development  of  trade  with  the  East,  more  and  more 
of  the  new  supplies  found  their  way  thither.  The 
most  rapid  rise  occurred  during  the  sixteenth  century. 

Money  and  its  Relation  to  Prices,  London  (Sonnenschein),  1900, 
New  York  (Scribner's),  p.  82  ff. 

^  Essays  in  Political  Economy,  2d  ed.,  No.  19. 


Sec.  2] 


STATISTICAL   VERIFICATION 


237 


§2 

The  stock  of  money  metals  at  any  time  in  any  country 
is  evidently  the  difference  between  the  total  product  and 
the  sum  of  the  consumption  and  the  net  export.  Jacob^ 
has  estimated  roughly  the  stock  in  Europe  at  various 
dates.  The  following  table  compares  the  estimated  me- 
talUc  stocks  in  Europe  with  the  estimated  price  levels : — 

Money  and  Prices 

Estimated  Product,  Consumption,  and  Stock  of  Precious  Metals  in 
Europe,  expressed  in  Millions  of  Dollars,  and  Price  Levels  ^ 


Date 

Product 

Consumption 
AND  Export 

Stock 

Prices 

1500  .... 
1600   .... 
1700   .... 
1800  .... 
1900  .... 

J        670 
1      1640 
1      4280 
1    13,000 

290 

740 

3880 

8960 

170 

550 

1450 

1850 

5890 

35 

75 

90 
100 
125  (?) 

1  William  Jacob,  F.R.S.,  An  Historical  Inquiry  into  the  Produc- 
tion and  Consumption  of  the  Precious  Metals,  2  vols.,  London  (Mur- 
ray) 1831  ;  Vol.  II,  p.  63.  See  also  Price,  Money  and  its  Relation 
to  Prices,  p.  78. 

*  The  estimates  of  the  product  and  stock  are  those  of  Jacob  and 
Soetbeer  (op.  cil.)  and  Del  Mar,  History  of  the  Precious  Metals, 
New  York  (Cambridge  Encyclopaedia  Co.),  1902,  p.  449.  The  price 
levels  (except  that  for  1900)  are  the  averages  of  those  of  Vicomte 
D'Avenel,  Histoire  Economique  de  la  Propriety  des  Salaires  et  des 
Denrees,  Vol.  I,  pp.  27  and  32,  Leber  and  Hanauer  (see  A.  Aupetit, 
Essai  sur  la  theorie  generate  de  la  monnaie,  Paris  (Guillaumin),  1901, 
p.  245),  the  three  estimates  being  each  reduced  to  100  per  cent  for 
the  last  quarter  of  the  eighteenth  century,  or  rather  1770-1790. 
The  figure  for  each  century  year  is  taken  as  the  average  of  the 
figures  given  by  the  three  authorities  for  the  preceding  and  succeed- 
ing quarter  century.     The  figure  for  1900  is  given  as  125  as  a  com- 


238  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

With  the  enormous  increase  in  the  quantity  of  the 
precious  metals,  small  wonder  if  prices  have  risen  ! 

We  see  that  there  has  been  a  general  increase  (1)  in  the 
stock  of  money  metals,  and  (2)  in  the  price  level,  and 
that  the  greatest  increase  of  each  was  in  the  sixteenth 
century.  We  find  also  that  the  prices  did  not  increase 
as  fast  as  the  quantity  of  money.  This  relative  slow- 
ness on  the  part  of  prices  was  to  be  expected,  because  of 
the  increased  volume  of  business.  This,  we  know,  must 
have  come  Vvdtli  increased  population  and  with  progress 
in  the  arts  —  especially  the  arts  of  trade  —  and  with 
development  in  transportation.  As  to  changes  in  the 
velocity  of  circulation  of  money  we  know  absolutely 
nothing. 

§3 

During  the  last  century  the  price  movements  have 
been  more  carefully  recorded  and  show  many  ups  and 
downs.  The  most  complete  statistics  (those  of  Sauer- 
beck) are  for  England.  They  are  represented  in  Figure 
11.^     As  is  well  known,  English  prices  were  inflated  by 

promise  between  widely  conflicting  results.  Leber,  Hanauer,  and 
D'Avenel  agree  fairly  well  and  D'Avenel  (^\Titing  in  1890  to  1894) 
finds  (p.  32)  the  "present"  price  level  in  France  to  be  double  what  it 
was  for  1776-1790,  which  would  make  the  required  figure  200.  The 
figures  for  England,  however,  of  Jevons  for  1782  to  1818,  Investi- 
gations in  Currency  and  Finance,  London  (Macmillan),  1884,  p.  144, 
combined  with  those  of  Sauerbeck  from  1818  to  the  present,  Course 
of  Average  Prices  in  England,  London  (King),  1908,  indicate  an  actual 
fall  of  prices,  the  figure  for  1900  being  on  the  above  basis  from  75 
to  80.  The  English  figures  are  so  m.uch  more  com-plete  than  the 
continental  figures  of  D'Avenel,  Leber,  and  Hanauer,  that  they  are 
given  more  weight,  and  125  seems  a  fair  rough  average  for  Europe. 
But  the  wide  discrepancies  between  the  various  figures  make  this, 
or  any  other  figure  which  might  be  chosen,  extremely  uncertain. 

^  The  figures  are  taken  from  various  numbers  of  the  Joiirnal  oj 
the  Royal  Statistical  Society.  For  many  years  Sauerbeck  has  pub- 
lished yearly  his  index  number  in  the  March  issue  of  this  journal. 


Sec.  3] 


STATISTICAL   VERIFICATION 


239 


the  issue  of  irredeemable  paper  during  the  Napoleonic 
wars.  This  period  of  the  paper  standard  extended 
from  1801  to  1820.  But  prices  in  paper  were  only 
shghtly  higher  than  prices  in  gold,  and  the  chief  price 


fX 

1(9 

1 

'ia 

I 

■ 

;:; 

:i 

^\ 

m 

:::: 

;^: 

prt 

Ih 

i 

:: 

ii 

::::: 

s 

1 

} 

1 

i 

; 

1 

;; 

^;; 

1 

i 

1 
:  + 

i 

MO 

n 

•e 
■«s 

1 

i 

5::::1 

i 

m 

i 

: 

i; 

l\\\ 

1 

h 

r.i 

m. 

-+fT^ 

T 

t 

1 

1 

■J 

1 

I 

:: 
::: 

1 

17^9  '&0O   *80S  l6tO     1513    ISSO  ISSS  1 


■  1635   1840  I 

Fig.  11. 


movements  (except  in  a  few  years)  were  but  slightly 
affected  by  the  existence  of  a  paper  standard.  The 
main  periods  of  price  movements  in  England  since 
1789  may  be  stated  as  follows:  — 

Prices  rose  1789-1809,  stock  increasing. 
Prices  fell    1809-1849,  stock  stationary. 
Prices  rose  1849-1873,  stock  increasing. 
Prices  fell    1873-1896,  stock  increasing  slightly. 
Prices  rose  1896-present,  stock  increasing. 

In  each  case  is  cited  the  movement  in  the  stock  of 
money  metals  in  Europe  as  given  in  the  table  of  Del  Mar.^ 

The  only  period  which  does  not,  at  first  glance,  agree 
with  what  we  might  expect  if  our  theory  of  price  levels 

1  History  of  the  Precious  Metals,  p.  449.  The  data  given  by  Del 
Mar  are  based  on  the  estimates  of  King,  Humbolt,  Jacob,  Tooke, 
Newmarch,  McCulIoeh,  and  himself.  The  dates  correspond  ap- 
proximately with  the  ends  of  the  periods  of  price  movements  as 
above  given.  The  following  figm-es  summarize  those  of  Del  Mar 
as  to  stock  (expressed  in  billions  of  dollars)  :  — 


1776 

1808 
1838 
1850 


1.4 
1.9 
1.3 
2.0 


1870, 
1876, 
1893 , 
1896, 


3.6 
3.7 
3.7 
4.5 


240  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

in  relation  to  money  is  correct,  is  the  period  1873-1896. 
Of  the  other  four  periods,  three  are  periods  of  rising 
prices  and  increasing  stocks.  The  fourth  is  a  period  of 
a  stationary  stock ;  and  since  the  volume  of  trade  un- 
doubtedly increased,  a  fall  of  prices  was  naturally  to 
be  expected. 

The  exceptional  period  1873-1896  —  a  period  of 
falling  prices  —  is  probably  to  be  accounted  for  by  the 
increasing  volume  of  trade  and  the  successive  demone- 
tization of  silver  by  various  countries. 

The  foregoing  parallelism  between  monetary  stocks 
and  prices  is  somewhat  remarkable  in  view  of  the  in- 
completeness of  the  data.^  In  the  table  there  are  lack- 
ing, not  only  exact  statistics  as  to  the  volume  of  trade 
and  all  statistics  whatever  of  velocity  of  circulation, 
but  also  statistics  of  the  volume  of  bank  notes,  govern- 
ment notes,  and  deposit  currency.  We  know,  however, 
that  modern  banking,  which  had  scarcely  developed  at 
all  before  the  French  Revolution,  developed  rapidly 
throughout  the  nineteenth  century.  It  is  also  known 
that  banking  and  deposit  currency  developed  more 
rapidly  during  the  third  period  in  the  table  (1849-1873) 
than  during  the  fourth  (1873-1896),2  which  fact  con- 
tributes somewhat  to  explain  the  contrast  between  the 
price  movements  of  these  two  periods. 

§4 

We  may,  therefore,  summarize  the  course  of  price 
movements  during  the  nineteenth  century  by  the  fol- 
lowing probable  statements :  — 

1.   Between  1789  and  1809  prices  rose  rapidly,  the 

*  Cf .  Albert  Aupetit,  Essai  sur  la  theorie  ginirale  de  la  monnaiet 
Paris  (Guillaumin),  1901,  pp.  271-285. 

*  See  Mulhall,  Dictionary  of  Statistics,  article  on  "Banks.!! 


Sec.  4]  STATISTICAL   VERIFICATION  241 

index  numbers  of  Jevons  moving  from  85  to  157  when 
prices  are  expressed  in  the  gold  standard,  or  161  when 
expressed  in  paper.^  That  is,  prices  practically  doubled 
in  twenty  years.  This  rise  was  due  to  the  increased 
stock  of  gold  and  silver,  which  in  turn  was  due  to  their 
large  production  during  this  period  as  compared  with 
the  periods  before  and  after.  The  production  of  silver 
was  especially  great. ^  The  Napoleonic  wars  with  their 
destruction  of  wealth  and  interference  with  trade  prob- 
ably exercised  some  influence  in  the  same  direction.^ 

2.  Between  1809  and  1849  prices  fell.  The  fall  was 
measured  by  Jevons  as  a  fall  from  157,  gold  (or  161 ,  paper) , 
to  64.  That  is,  in  forty  years  prices  were  reduced  to 
less  than  half,  or,  to  be  more  exact,  to  two  fifths.  This 
fall  in  prices  was  presumably  due  to  the  lull  in  the  pro- 
duction of  the  precious  metals,  which  prevented  the 
aggregate  stock  from  keeping  pace  with  the  volume  of 
business.  Indeed,  the  aggregate  stock  remained  station- 
ary while  the  volume  of  business  increased.  Even  the 
development  of  bank  currency  was  insufficient  to  offset 
the  continued  increase  in  the  volume  of  business.  It  is 
interesting  to  observe  that  this  period  of  falling  prices 
was  interrupted  by  a  temporary  rise  after  1833,  which 
Jevons  was  at  a  loss  to  account  for,  but  which  was  ap- 
parently due  to  the  inflow  of  Russian  gold  after  the 
discoveries  of  gold  in  Siberia  in  1830.* 

3.  Between  1849  and  1873  (although  with  two  nota- 
ble interruptions)  prices  rose.     They  rose,  according 

*  Jevons,  Investigations  in  Currency  and  Finance,  London  (Mae- 
millan),  1884,  p.  144. 

''See  Magee,  "World's  Production  of  Gold  and  Silver,"  Journal 
of  Political  Economy,  January,  1910,  pp.  54,  56. 

'  See  Harrison  H.  Brace,  Gold  Production  and  Future  PriceSf 
New  York  (Bankers'  Publishing  Co.)  1910,  pp.  16  and  17. 

*  Price,  Money  and  its  Relation  to  Prices,  p.  112. 


242  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

to  Jevons's  figures  supplemented  by  Sauerbeck's/  from 
64  to  86,  and  according  to  Sauerbeck's  alone,  from  74 
to  111.  That  is,  in  24  years  prices  increased,  according 
to  one  calculation,  by  one  third;  according  to  another, 
by  one  half.  This  rise  was  presumably  in  consequence 
of  the  gold  inflation  following  the  famous  California  gold 
discoveries  in  1849  and  Australian  discoveries  in  1851 
and  1852.  The  simultaneous  rapid  development  of 
banking  contributed  to  the  same  result  in  spite  of  the 
continued  increase  in  trade. 

4.  Between  1873  and  1896  prices  fell.  This  fall  was 
presumably  due  to  the  slackening  in  the  production  of 
gold ;  to  the  adoption  of  the  gold  standard  by  nations 
previously  on  a  silver  basis,  and  the  consequent  with- 
drawal of  gold  by  these  new  users  from  the  old ;  to  the 
arrest  of  the  expansion  of  silver  money  consequent  on 
the  closure  of  mints  to  silver ;  to  the  slackening  in  the 
growth  of  banking;  and  to  the  ever  present  growth  of 
trade.^ 

During  the  long  fall  of  prices  from  1873  to  1896,  coun- 
try after  country  adopted  the  gold  standard.  We  have 
already  seen  that  Germany  adopted  the  gold  standard 

^  This  rise  is  found  by  adding  to  Jevons's  table,  which  ends  in 
1865,  a  fictitious  figure  (86)  for  1873,  calculated  to  be  in  the  ratio 
to  the  1865  figure  (78),  which  Sauerbeck's  figure  for  1873  (111) 
bears  to  his  figure  for  1865  (101). 

-  It  is  not  that  the  left-hand  side  of  the  equation  did  not  increase, 
but  that  it  did  not  increase  so  fast  as  trade  ;  therefore  prices  fell. 
Laughlin  seems  to  think  he  is  overthrowing  Mill's  position  that 
credit  acts  like  money  on  prices  (an  increase  of  credit  raising  prices, 
other  things  equal),  by  appealing  to  the  fact  of  an  enormous  growth 
of  deposit  currency  in  this  period  which  had  not  raised  prices  nor 
prevented  their  fall.  But  if  trade  increased  even  faster  (and  Laugh- 
lin himself  asserts  an  increase  of  trade,  though  he  denies  that  it  is  a 
satisfactory  answer),  then  a  fall  of  prices  was  not  opposed  to,  but 
entirely  consistent  with.  Mill's  theory.  See  Laughlin,  The  Principles 
of  Money,  New  York  (Scribner),  1903,  pp.  319  and  320. 


Sec.  4]  STATISTICAL   VERIFICATION  243 

in  1871-1873,  thus  helping  to  render  impossible  the 
maintenance  of  bimetallism  by  the  Latin  Union.  The 
Scandinavian  monetary  union  adopted  the  gold  stand- 
ard in  1873.  Between  that  date  and  1878  the  countries 
of  the  Latin  Union  suspended  the  free  coinage  of  silver 
and  came  practically  to  a  gold  basis.  In  the  United 
States  the  legislation  of  1873  signified  that  with  re- 
sumption (which  took  place  in  1879),  the  country  would 
come  to  a  gold  basis,  although  no  considerable  amount 
of  silver,  except  for  small  change,  had  been  coined  here 
for  several  decades  previously.  The  Netherlands  virtu- 
ally adopted  the  gold  standard  in  1875-1876,  Egypt  in 
1885,  Austria  in  1892,  India  in  1893,  Chih  in  1895, 
Venezuela  and  Costa  Rica  in  1896,  Russia,  Japan,  and 
Peru  in  1897,  Ecuador  in  1899,  and  Mexico  in  1905.  In 
fact,  most  countries  of  importance  have  now  definitely 
adopted  the  gold  standard. 

The  preceding  figures  apply  only  to  gold  countries. 
But  in  1873  gold  and  silver  countries,  as  it  were,  fell 
asunder.  It  is  interesting,  therefore,  to  inquire  whether 
the  movement  of  prices  in  gold  countries  was  parallel 
or  antithetical  to  that  in  silver  countries.  As  might  be 
expected,  we  find  it  antithetical.  The  demonetization 
of  silver  in  gold  countries  made  a  greater  amount  of  that 
metal  available  for  silver  countries.  Accordingly,  we 
find  that  prices  rose  in  India  from  107  in  1873  to  140  in 
1896,'  in  Japan  from  104  in  1873  to  133  in  1896,^  and  in 

^  F.  J.  Atkinson,  "Silver  Prices  in  India,"  Journal  of  the  Royal 
Statistical  Society,  March,  1897,  p.  92.  The  figures  for  1893,  1894, 
1895,  and  1896  were  lowered  by  the  closure  of  the  Indian  mint  to 
silver  in  1893. 

2  The  figures  from  1873  to  1893  are  from  Japanese  Monetary 
Reports,  1895,  translated  for  me  by  Mr.  Sakata  of  Yale  University. 
The  figures  for  1894,  1895,  1896  were  also  from  official  Japanese 
soxirces  provided  by  Japanese  students. 


244  THE    PURCHASING    POWER   OF   MONEY       [Chap.  XI 

China  from  100  in  1874  to  109  in  1893.i  These  figures, 
although  not  as  reliable  and  representative  as  the  figures 
for  gold  countries,  agree  in  indicating  a  rise  of  prices. 
The  amount  of  rise  is  differently  indicated,  ranging 
roughly  from  10  per  cent  to  35  per  cent.  The  following 
table  shows  the  contrast  between  the  gold  and  silver 
countries  as  between  1873-1876  and  1890-1893,  the 
last  year  being  that  of  the  closure  of  the  Indian  mint  to 
silver.^ 

Prices  in  Gold  and  Silver  Countries  ' 


Gold 

Silver 

1873-1876     

100 

78 

100 

1890-1893     

117 

We  see  that  gold  prices  fell  a  little  more  than  20  per 
cent  and  that  silver  prices  rose  a  little  less  than  20  per 
cent.^ 

If  some  way  had  been  contrived  by  which  gold  and 
silver  could  have  been  kept  together  (say  by  world-wide 

^  From  the  Japanese  Report  mentioned  in  the  above  note. 

^  The  figures  for  prices  in  India  are,  of  course,  too  meager  and 
local  to  be  of  as  great  value  as  the  corresponding  index  numbers  for 
Europe  and  America.  Cf.  figures  cited  by  J.  Barr  Robertson's 
article  (1903),  Report  of  Commission  on  International  Exchange,  58th. 
Congress,  2d  Session,  H.  R.  Document  144,  Washington,  1903^ 
pp.  357-378. 

^  Irving  Fisher,  "Prices  in  Silver  Countries,"  Yale  Review,  May, 
1897,  p.  79.  The  index  numbers  for  gold  countries  are  based  on 
those  of  Sauerbeck  for  England,  Soetbeer,  Heintz,  and  Conrad  for 
Germany,  and  Falkner  (Aldrich  Report)  for  the  United  States. 
Those  for  silver  countries  are  from  Atkinson  for  India  and  the 
Report  of  the  Japanese  Currency  Commission  above  referred  to. 

*  We  may  remark  in  passing  that  this  divergence  between  the 
two  sets  of  prices  is  somewhat  more  than  the  divergence  between 
gold  and  silver  themselves. 


Sec.  4]  STATISTICAL   VERIFICATION  245 

bimetallism),  prices  would  not  have  fallen  so  much  in 
gold  countries,  or  risen  so  much  (if  at  all)  in  silver  coun- 
tries, but  would  probably  have  fallen  in  gold  countries 
slightly  —  probably  about  10  per  cent  up  to  1890-1893 
and  more  up  to  1896.  This  is  because  the  stocks  of 
specie  in  silver  countries  were  less  than  half  those  in  gold 
countries  ^  (including  those  with  the  "  limping  stand- 
ard "  from  left-over  silver) ;  so  that  had  there  been  a 
transfer  of  a  given  amount  of  silver  from  the  silver 
Orient  to  the  gold  Occident,  this  would  have  affected 
Oriental  prices  about  twice  as  much  as  Occidental. 

The  transition  of  India  from  the  silver  to  the  gold 
side  has  left  about  nine  tenths  ^  of  the  specie  (gold  and 
overvalued  silver)  in  the  gold  column.  In  other  words, 
the  world  is  now  practically  on  a  gold  basis.  The  result 
has  been  to  make  Indian  prices  move  in  sympathy  with 
European  prices,^  instead  of  in  opposition. 

5.  From  1896  to  the  present,  prices  have  been  rising 
because  of  the  extraordinary  rise  in  gold  production  and 
the  consequent  increase  in  money  media  of  all  kinds. 
The  gold  of  South  Africa  combined  with  the  gold  from 
the  rich  mines  of  Cripple  Creek  and  other  parts  of  the 
Rocky  Mountain  Plateau,  and  reenforced  by  gold  from 
the  Klondike,  caused,  and  is  still  causing,  a  repetition 
of  the  phenomenon  of  half  a  century  ago. 

That  there  has  been  a  distinct  rise  in  prices  is  evident 
from  the  figures  of  all  index  numbers.  Those  of  The 
Economist,  Sauerbeck,  Dun,  the  Labor  Bureau  Reports, 
and  Bradstreet  are  given  on  the  following  page. 

1  See  Muhleman,  Monetary  Systems  of  the  World,  New  York 
(Nicoll),  1897,  p.  177. 

2  See  Muhleman,  ibid. 

'  See  J.  B.  Robertson,  "Variations  in  Indian  Price  Levels  since 
1861  expressed  in  Index  Numbers,"  Department  oj  Commerce  and 
Industry  (Government  of  India). 


246 


THE    PURCHASING   POT\^R   OF  MONEY       [Chap.  XI 


English 

American 

Close  of  Dec. 

Economist 

Sauerbeck 

Dun 

Labor  Bureau 

Bradstreet 

1896    .     . 

1950 

61 

74 

90 

59 

1897    .    . 

1890 

62 

72 

90 

61 

1898    .     . 

1918 

64 

77 

93 

66 

1899    .     . 

2145 

68 

85 

102 

72 

1900    .     . 

2126 

75 

91 

111 

79 

1901    .     . 

1948 

70 

91 

109 

76 

1902    .     . 

2003 

69 

102 

113 

79 

1903    .     . 

2197 

69 

99 

114 

79 

1904    .     . 

2136 

70 

97 

113 

79 

1905    .     . 

2342 

72 

98 

116 

81 

1906    .     . 

2499 

77 

105 

123 

84 

1907    .     . 

2310 

80 

130 

89 

1908    .     . 

2197 

73 

123 

80 

1909    .     . 

2373 

74 

127 

85 

The  high  points  of  1900  and  1907,  as  compared  with 
the  low  level  of  1896,  must  be  regarded  as  at  least  partly 
due  to  expansion  of  credit.  The  fairest  comparison  (to 
eliminate  the  effects  of  undue  changes  in  credit)  is  per- 
haps that  of  the  years  1896,  1903,  and  1909.  That  the 
rise  of  prices  has  been  world  wide  is  evidenced  not  only 
by  index  numbers,  which  are  only  available  for  a  limited 
number  of  countries,  but  by  general  impressions  of  con- 
sumers and  by  special  reports  and  investigations.^ 

The  period  1896-1909  for  the  United  States  will  be 
studied  in  more  detail  in  the  following  chapter. 

§5 

It  will  be  seen  that  the  history  of  prices  has  in  sub- 
stance been  the  history  of  a  race  between  the  increase  in 
media  of  exchange  (M  and  M')  and  the  increase  in 
trade  (T),  while  (we  assume)  the  velocities  of  circulation 

^See  Report  of  the  Select  Committee  on  Wages  and  Prices  of  Comr- 
modities.  Senate  Report  912,  61st  Congress,  2d  Session,  1910. 


Sec.  5]  STATISTICAL   VERIFICATION  247 

were  changing  in  a  much  less  degree.  Knowing  Uttle  of 
the  variations  in  the  development  of  trade,  we  may  ten- 
tatively assume  a  steady  growth,  and  pay  chief  atten- 
tion to  the  variations  of  circulating  media.  Sometimes 
the  circulating  media  shot  ahead  of  trade  and  then  prices 
rose.  This  was  undoubtedly  the  case  in  the  periods 
numbered  1,  3,  and  5  of  the  five  periods  just  considered. 
Sometimes,  on  the  other  hand,  circulating  media  lagged 
behind  trade  and  then  prices  fell.  This  must  have 
been  the  case  in  the  periods  numbered  2  and  4. 

It  is  important  to  emphasize  at  this  point  a  fact 
mentioned  in  a  previous  chapter ;  namely,  that  the 
breakdown  of  bimetallism  and  the  consequent  division 
of  the  world  into  a  gold  section  and  a  silver  section 
have  made  each  section  more  sensitive  than  before  to 
fluctuations  in  the  production  of  the  precious  metals. 
The  present  flood  of  gold  can  spread  itself  only  over 
the  gold  section  of  the  world,  and  not  over  the  whole 
world  as  was  virtually  the  case  with  the  Calif ornian  gold 
immediately  after  1849.  At  that  time  gold  displaced 
silver  in  bimetallic  France  and  sent  it  to  the  Orient. 
In  this  way  the  Orient  afforded  relief  for  bimetallic 
countries  by  draining  off  silver  and  making  room  for 
gold;  and  the  bimetallic  countries  thereby  afforded 
relief  to  gold  countries  also. 

Since  1873,  therefore,  the  gold  reservoir  of  Europe 
and  America  has  been  separated  from  the  silver  reser- 
voir of  the  East,  with  the  consequence  that  the  Euro- 
pean and  American  reservoir  level  has  been  made  more 
sensitive  to  either  a  scarcity  or  a  superabundance  of 
gold.  The  result  has  been  to  aggravate  both  the  fall  of 
prices  from  1873  to  1896  and  the  present  rise,  although 
the  later  effect  is  mitigated  by  the  previous  extension 
of  the  gold  standard. 


248  THE    PURCHASING   POWER  OF  MONEY       [Chap.  XI 

§6 

The  outlook  for  the  future  is  apparently  toward  a 
continued  rise  of  prices  due  to  a  continued  increase  in 
the  gold  supply.  To-day  almost  as  much  gold  is  pro- 
duced every  year  as  was  produced  in  the  whole  of  the 
16th  century. 

The  most  careful  review  of  present  gold-mining  con- 
ditions shows  that  we  may  expect  a  continuance  of  gold 
inflation  for  a  generation  or  more.  'Tor  at  least 
thirty  years  we  may  count  on  an  output  of  gold  higher 
than,  or  at  least  comparable  to,  that  of  the  last  few 
years."  ^  This  gold  will  come  from  the  United  States, 
Alaska,  Mexico,  the  Transvaal,  and  other  parts  of 
Africa  and  Australia,  and  later  from  Colombia,  Bolivia, 
Chili,  the  Ural  Province,  Siberia,  and  Korea.  It  must 
be  remembered  that  it  is  the  stock  of  gold  and  not  the 
annual  production  which  influences  the  price  level; 
and  that  the  stock  will  probably  continue  to  increase 
for  many  years  after  the  production  has  begun  to 
decline,  —  as  long,  in  fact,  as  production  keeps  above 
consumption. 

A  lake  continues  to  rise  long  after  the  freshet  which 
feeds  it  has  reached  its  maximum.  So  the  stock  of 
gold  will  continue  to  increase  long  after  the  annual 
production  of  gold  has  stopped  increasing.  Whether 
or  not  prices  will  continue  to  rise  depends  on  whether 
the  increase  in  gold  and  the  circulating  media  based 
on  gold  continues  to  exceed  the  growth  of  trade.  It  is 
the  relation  of  gold  to  trade  that  chiefly  affects  prices. 
Even  if  the  stock  of  gold  should  increase  for  many  years, 
prices  may  not  rise ;  for  trade  may  increase  still  faster. 

1  L.  de  Launay,  The  World's  Gold,  English  translation,  New  York 
(Putnam),  1908,  p.  227. 


Sec.  6]  STATISTICAL   VERIFICATION  249 

If  the  annual  additions  of  gold  to  the  total  stock  remain 
constant  and  consequently  the  stock  continually  in- 
creases, the  ratio  between  the  constant  annual  addi- 
tion and  the  increasing  stock  will  evidently  decrease, 
and  the  increase  in  stock  will  count  for  less  and  less  in 
raising  prices.^ 

It  is  difficult  to  predict  the  future  growth  of  trade  and 
therefore  impossible  to  say  for  how  long  gold  expansion 
will  keep  ahead  of  trade  expansion.  That  for  many 
years,  however,  gold  will  outrun  trade  seems  probable, 
for  the  reason  that  there  is  no  immediate  prospect  of 
a  reduction  in  the  percentage  growth  of  the  gold  stock, 
nor  of  an  increase  in  the  percentage  growth  of  trade. 
Not  only  do  mining  engineers  report  untold  workable 
deposits  in  outlying  regions  (for  instance  a  full  billion 
of  dollars  in  one  region  of  Colombia  alone),  but  any 
long  look  ahead  must  reckon  with  possible  and  probable 
cheapening  of  gold  extraction.  The  cyanide  process 
has  made  low  grade  ores  pay.  If  we  let  imagination 
run  a  little  ahead  of  our  times,  we  may  expect  similar 
improvements  in  the  future  whereby  still  lower  grades 
may  be  worked  or  possibly  the  sea  compelled  to  give 
up  its  gold.  Like  the  surface  of  the  continents,  the 
waters  of  the  sea  contain  many  thousand  times  as  much 
gold  as  all  the  gold  thus  far  extracted  in  the  whole 
history  of  the  world.  It  is  to  be  hoped  that  the  knowl- 
edge of  how  to  get  this  hidden  treasure  may  not  be 
secured.  To  whatever  extent  inventors  and  gold 
miners  might  be  enriched  thereby,  scarcely  a  worse 
economic  calamity  can  be  imagined  than  the  resulting 

'  Cf.  Jevons,  Investigations  in  Currency  and  Finance,  London 
(Macmillan),  1884,  pp.  64,  65,  66;  also  Harrison  H.  Brace,  Gold 
Production  and  Future  Prices,  New  York  (Bankers'  Publishing  Co.), 
1910,  p.  113. 


250  THE    PURCHASING   POWER  OF  MONEY       [Chap.  Xl 

depreciation.  It  may  be,  however,  that  only  by  such  a 
calamity  can  the  nations  of  the  world  be  aroused  to  the 
necessity  of  getting  rid  of  metallic  standards  altogether. 

§7 

We  have  briefly  summarized  the  history  of  price 
movements  since  the  discovery  of  America  and  shown 
their  relation  to  the  stock  of  the  precious  metals.  But, 
as  we  have  emphasized  in  previous  chapters,  the  pre- 
cious metals  do  not  include  all  forms  of  circulating 
media.  Paper  money  and  bank  deposits  have  come 
during  the  nineteenth  century  to  occupy  very  important 
places  in  currency  systems. 

We  shall  not  attempt  any  complete  review  of  the 
effects  of  paper  money  on  prices.  The  best  that  can 
be  done  is  to  mention  briefly  the  most  striking  cases  of 
paper  money  inflation  and  contraction.  These  are  all 
cases  of  irredeemable  paper  money.  When  paper 
money  is  redeemable,  its  possible  increase  is  restricted 
by  that  fact  and,  what  is  more  important,  the  effects  of 
the  increase  are  dissipated  over  so  large  an  area  as  to 
have  little  perceptible  effect  on  prices.  This  dissipa- 
tion takes  place  through  the  export  of  specie  from  the 
country  in  which  the  paper  issues  occur.  Though 
the  paper  cannot  be  itself  exported,  it  can  displace 
gold  or  silver,  which  amounts  to  the  same  thing  so  far 
as  spreading  out  the  effect  on  prices  is  concerned. 

But  when  the  paper  is  irredeemable,  after  specie  has 
been  expelled  from  circulation  (whether  by  export, 
melting,  or  hoarding  in  anticipation  of  disaster)  there 
is  no  such  spreading-out  effect.  The  effects  on  prices 
are  then  entirely  local  and  therefore  greatly  magnified.^ 

1  See  Ricardo,  Essay  on  the  "High  Price  of  Bullion,"  Works, 
2d  ed.,  London  (Murray),  1852,  p.  278. 


Sec.  7]  STATISTICAL   VERIFICATION  251 

The  consequence  is  that  the  most  striking  examples 
of  price  inflation  are  cases  of  irredeemable  paper  money. 
The  rise  of  prices  is  often  still  further  aggravated  by 
the  gradual  substitution  of  other  and  better  money 
or  resort  to  barter,  which  further  restricts  the  sphere 
in  which  the  paper  is  used  and  within  that  sphere  makes 
it  the  more  redundant.  Where  the  paper  money  is 
looked  upon  with  disfavor,  for  whatever  reason  — 
whether  because  its  promised  redemption  has  been 
indefinitely  postponed,  or  simply  because  of  the  bare 
fact  that  it  is  depreciating,  or  because  of  any  other 
consideration  —  its  sphere  of  use  is  restricted.^  Credi- 
tors and  tradesmen  avoid  taking  it  if  they  can,  by 
"contracting  out"  in  advance;  by  barter;  by  fixing 
a  double  set  of  prices,  one  in  paper  and  the  other  in 
some  other  money;  and  by  outright  refusal.  In  the 
end  it  may  happen  that  the  paper  ceases  to  be  used  at 
all.  In  that  case  its  value  depreciates  indefinitely  and 
therefore  prices  (so  far  as  still  expressed  in  terms  of 
paper)  rise  indefinitely. 

Whatever  the  situation,  the  equation  of  exchange 
continues  to  hold  true  though  its  significance  becomes 
of  less  importance,  because  T,  instead  of  comprising 
practically  all  trade,  comes  to  mean  only  that  disappear- 
ing portion  of  trade  still  transacted  by  means  of  paper 
money. 

The  value  of  irredeemable  paper  money  is,  therefore, 
extremely  precarious.  If  once  it  starts  depreciating  — 
from  whatever  cause  —  it  is  likely  to  depreciate  further, 
not  simply  because  of  the  ever  present  temptation  to 
further  issue,  but  also  because  of  a  growing  public 

1  See  Francis  A.  Walker,  Money,  New  York  (Holt),  1878,  p.  199. 
Cf.  Joseph  French  Johnson,  Money  and  Currency,  Boston  (Ginn), 
1906,  p.  269. 


252  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

sentiment  against  it  which  sooner  or  later  restricts  its 
use.^  In  many  cases  the  irredeemable  paper  money- 
continues  to  be  used  with  sufficient  acceptability  to  give 
it  a  virtual  monopoly  as  a  medium  of  exchange. 

Although  theoretically  irredeemable  paper  money 
may  be  the  cheapest  and  most  easily  regulated  form 
of  currency,  and  although,  in  some  cases,  it  has  remained 
a  stable  currency  for  a  considerable  period,  the  lesson 
of  history  is  emphatically  that  irredeemable  paper 
money  results  in  monetary  manipulation,  business  dis- 
trust, a  speculative  condition  of  trade,  and  all  the  evils 
which  flow  from  these  conditions. 

§8 

One  of  the  early  paper-money  schemes  was  that  of 
John  Law,  who  established  a  bank  of  issue  in  France 
in  1716.  Two  years  later  (December  4, 1718),  the  bank 
was  taken  over  by  the  Crown.  Soon  shrewd  traders 
were  acquiring  specie  for  notes  and  exporting  the 
specie  secretly,  although  exportation  of  specie  was  illegal. 
May  27,  1720,  only  four  years  after  its  establishment, 
the  bank  stopped  payment  of  specie.  By  November  of 
the  very  same  year  the  paper  had  fallen  to  one  tenth  of 
its  par  value,  and  after  this  it  became  utterly  worthless. 

The  case  of  the  assignats  of  the  French  Revolution  is 
classic.^  It  was  in  December,  1789,  that  the  first  issue, 
four  hundred  million  francs,  was  ordered,  based  osten- 
sibly on  the  landed  property  of  the  nation.  The  notes 
were  issued  in  April,  1790,  and  bore  3  per  cent  interest. 
According  to  the  original  plan,  all  of  the  assignats  received 

1  Cf .  the  mention  of  this  influence  on  depreciation  in  the  Bxxllion 
Report,  III. 

2  For  the  following  facts,  see  Andrew  D.  White,  Paper  Money 
Inflation  in  France,  Economic  Tracts,  No.  VII,  No.  3  of  Series,  1882. 


Sec.  8]  STATISTICAL   VERIFICATION  253 

in  payment  for  land  were  to  be  burned.  But  original 
plans  seem  never  to  be  carried  out  with  respect  to  paper 
money.  Instead,  a  hundred  millions  were  reissued  in 
the  form  of  small  notes.  Prices  began  to  rise.  In 
June  of  the  year  1791,  six  hundred  millions  more  were 
issued.  Depreciation  to  the  extent  of  8  to  10  per  cent 
immediately  followed.  Specie  was  rapidly  disappear- 
ing. Another  three  hundred  millions  of  francs  were 
ordered  in  December,  1791.  By  February,  the  assig- 
nats  were  over  30  per  cent  below  par.  In  April,  1792, 
came  a  decree  for  the  issue  of  three  hundred  millions 
more,  and  in  July  for  the  same  amount  additional. 
Most  prices  were  very  high,  but  wages  seem  to  have 
still  remained  at  the  level  of  1788.  By  December  14 
of  1792,  thirty-four  hundred  million  francs  had  been 
issued  in  assignats,  of  which  six  hundred  millions  had 
been  burned,  leaving  twenty-eight  hundred  millions  in 
circulation.  Laws  were  enacted  to  fix  maximum  prices, 
but  were  evaded.  By  1796,  forty-five  billion  francs  had 
been  issued,  of  which  thirty-six  billions  were  in  circula- 
tion. In  February  of  that  year  the  gold  louis,  of  25 
francs,  was  worth  7200  francs  in  assignats ;  and  the 
assignats  were  worth  ^Is  of  P^-^-  A.  new  kind  of  paper 
money,  the  mandats,  was  next  issued,  but  soon  fell  to 
5  per  cent  of  its  nominal  value.  In  the  end  the  twenty- 
five  hundred  million  mandats  and  the  thirty-six  billion 
assignats  were  repudiated  and  became  entirely  worth- 
less. 

§9 

England's  experience  with  irredeemable  paper  money 
was  more  temperate.  Under  the  stress  of  the  Napole- 
onic wars,  the  Bank  of  England  suspended  cash  pay- 
ments in  1797.  This  nullified  the  force  which  auto- 
matically limited   overissue.     The  bank  resumed  cash 


254 


THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 


payments  in  1821.  During  much  of  the  intervening 
period  of  paper  money,  prices  in  paper  were  very  high. 
The  following  table  of  Jevons  shows  the  relative  prices 
in  notes  and  specie  from  1801  to  1820  :  ^  — 


Ybae 

Gold  Standard 

Paper  Standard 

1801 

140 

153 

1802 

110 

119 

1803 

125 

128 

1804 

119 

122 

1805 

132 

136 

1806 

130 

133 

1807 

129 

132 

1808 

145 

149 

1809 

157 

161 

1810 

142 

164 

1811 

136 

147 

1812 

121 

148 

1813 

115 

149 

1814 

114 

153 

1815 

109 

132 

1816 

91 

109 

1817 

117] 

120 

1818 

132 

135 

1819 

112 

117 

1820 

103 

106 

The  causes  of  the  rise  of  prices  were  discussed  in 
the  famous  BuUion  Report.  The  general  conclusion 
reached  was  that  a  "rise  of  the  market  price  of  gold 
above  its  mint  price  will  take  place,"  if  the  local  cur- 
rency of  any  particular  country,  ''being  no  longer  con- 
vertible into  gold,  should  at  any  time  be  issued  to  excess. 
That  excess  cannot  be  exported  to  other  countries,  and, 
not  being  convertible  into  specie,  it  is  not  necessarily 
returned  upon  those  who  issued  it;  it  remains  in  the 
channel  of  circulation,  and  is  gradually  absorbed  by 

1  Investigations  in  Currency  and  Finance,  London  (Macmillan), 
1884,  p.  144. 


Sec.  10]  STATISTICAL   VERIFICATION  255 

increasing  the  prices  of  all  commodities.  An  increase 
in  the  quantity  of  the  local  currency  of  a  particular 
country  will  raise  prices  in  that  country  exactly  in  the 
same  manner  as  an  increase  in  the  general  supply  of  pre- 
cious metals  raises  prices  all  over  the  world.  By  means 
of  the  increase  of  quantity,  the  value  of  a  given  portion 
of  that  circulating  medium,  in  exchange  for  other  com- 
modities, is  lowered.  In  other  words,  the  money  prices 
of  all  other  commodities  are  raised  —  that  of  bulhon 
with  the  rest."  This  is  an  excellent  statement  of  the 
philosophy  of  irredeemable  paper  money  when  that 
money  is  sufficiently  within  bounds  to  remain  in  general 
use.  No  mention  is  made  of  partial  or  complete  aban- 
donment of  use  because  of  worthlessness.  The  reason 
is  doubtless  that  in  England  the  paper  money  never 
reached  this  pass,  as  it  undoubtedly  did  in  many  in- 
stances in  France,  Austria,  America,  and  elsewhere. 

§10 

Austrian  experience  with  paper  money  is  instructive.* 
Like  so  many  of  the  European  banks,  that  of  Austria 
was  used  by  the  government  as  an  instrumentality  for 
obtaining  loans.  This  was  done  by  allowing  the  bank 
to  issue  large  sums  in  notes.  The  wars  with  Napoleon 
demanded  supplies,  and  during  these  wars  the  issue  was 
largely  increased.  In  1796  the  note  issue  was  47,000,000 
gulden;  in  1800  it  was  200,000,000;  in  1806,  it  was 
449,000,000.  The  notes  were  much  below  par.  In 
1810  the  bank  notes  fell  successively  to  ^,  |  and  about 
^of  par.  In  1811  a  proclamation  openly  valued  them 
at  one  fifth  of  their  nominal  value  and  decreed  their 
exchange  at  this  rate  for  redemption  notes,  called  the 

*  See  W.  G.  Sumner,  History  of  American  Currency,  New  York 
(Holt),  1874,  Chapter  III. 


256  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

Viennese  legal  tender,  which  became  the  Austrian 
legal-tender  currency.  But  even  these  new  issues  soon 
fell  to  2  16  of  their  face  value  (May,  1812)  and  3^^  of  their 
face  value  (June,  1812),  while  the  bank  notes  were  at 
1G90  to  100  in  silver.  New  issues  were  added  under  a 
difTerent  name  until,  in  1816,  the  amount  of  paper 
money  was  over  638,000,000,  with  prices,  of  course, 
tremendously  inflated.  In  1816  was  founded  the  Aus- 
trian national  bank,  which  was  intended  to  draw  in  the 
paper  money.  From  time  to  time  thereafter  the  amount 
of  paper  circulation  was  reduced,  but  not  without  occa- 
sional relapses.  At  the  present  time  Austria  has  no 
paper  money  which  is  not  at  par. 

§11 
Many  of  the  American  colonies  had  experience  with 
paper  money.  In  fact,  one  of  the  grievances  against 
England  was  the  parliamentary  prohibition  of  paper 
money  issues  !  In  practically  all  cases  ^  there  was  over- 
issue and  depreciation.  This  was  true,  for  example,  in 
Massachusetts,  where  paper  money  was  issued  to  pay 
the  expenses  of  the  expeditions  against  Canada,^  and 
in  Rhode  Island,^  which  suffered  more,  perhaps,  from 
paper  money  than  any  of  the  others.  Following  are 
figures  for  Rhode  Island  taken  from  the  account  book 
of  Thomas  Hazard  (the  entries  and  memoranda  ex- 
tending from  1750  to  1785),  which  show  the  height  and 
variabihty  of  prices.^ 

^  Pennsylvania  seems  to  have  been  an  exception. 

2  W.  G.  Sumner,  History  of  American  Currency,  Chapter  I. 

» Ibid. 

*  Rowland  Hazard,  Sundry  prices  taken  from  Ye  Account  Book 
of  Thomas  Hazard,  son  of  Robt.  Wakefield,  R.I.  (Times  Print), 
1892. 


Sec.  11] 


STATISTICAL   VERIFICATION 


257 


1755.    Hay  £20  per  Load 
Corn  per  Bushel  Butter  per  Pound 


1751 
1758 
1762 

25  s. 

50  s. 

100  s. 

Wool  per  Pound 

1751 
1760 

1752 
1756 
1759 
1768 

8  s. 

12  s. 

28  s. 

32  s. 

1750 
1753 

1774 

7  s. 
16  s. 


Potatoes  per  Bushel 


10  s. 
20  s. 
35  s. 


We  had  also  during  the  Revolution  a  national  expe- 
rience with  Continental  paper  money  which  gave  rise 
to  the  derogatory  phrase,  still  current,  "not  worth  a 
continental."  Depreciation  began  almost  from  the 
moment  of  issue  (1775),  and  finally  the  money  was 
recognized  by  Congress  itself  to  have  reached  -^q  of  the 
nominal  value. ^  All  prices,  of  course,  were  tremen- 
dously high.  Even  the  new  tenor  paper  given  for  the 
old  emissions  at  the  rate  of  a  dollar  for  forty  ^  declined 
rapidly  in  value.  A  bushel  of  wheat  was  worth,  at 
one  time,  seventy-five  dollars,  coffee  four  dollars  a 
pound,  and  sugar  three  dollars  a  pound.^  It  is  inter- 
esting to  observe  that,  in  this  case,  the  depreciation 
seems  to  have  been  accentuated  far  beyond  what  mere 
overissue  tended  to  produce,  by  a  distrust  of  the  money 
and  a  refusal  to  receive  it  in  trade.  Several  classes  were 
disinclined  to  receive  it  to  begin  with,  and  as  confidence 
waned,  the  number  who  were  unwilling  to  receive  it 
increased.  Barter  frequently  took  the  place  of  trade 
with  money.^ 

The  depreciation  was  doubtless  much  greater  because 

^  See  Albert  S.  BoUes,   Financial  History  of  the   United  States, 
Vol.  I,  from  1774  to  1789,  New  York  (Appleton),  1879,  p.  135. 
» Ibid.,  pp.  137  and  138.        » Ibid.,  p.  141.        *  Ibid.,  Chapter  IX 

8 


258  THE    PURCHASING    POWER   OF   MONEY       [Chap.  XI 

the  paper  money  of  various  colonies  helped  to  overflow 
the  circulation,  competing  with  the  congressional  money 
and  limiting  its  sphere  of  circulation. 

§12 

The  effects  were  so  disastrous  that,  in  the  Constitu- 
tion of  the  United  States,  a  provision  was  incorporated 
prohibiting  any  state  from  issuing  "bills  of  credit." 
But,  during  the  Civil  War,  the  temptation  again  came 
to  resort  to  this  easy  way  of  securing  means  of  pay- 
ment ;  and  the  federal  government  itself  issued  United 
States  notes  or  "greenbacks."  The  banks  had  already 
suspended  specie  payments  so  that  gold  was  at  a  slight 
premium  in  bank  paper.  ^ 

These  greenbacks  were  issued  from  time  to  time  dur- 
ing the  war  with  resulting  depreciation  as  their  quantity 
increased,  —  a  depreciation  greater  or  less  also  accord- 
ing as  failure  or  success  of  the  Union  armies  affected 
confidence  in  the  paper  money.  The  amounts  issued 
were:  $150,000,000  by  the  act  of  February  25,  1862; 
$150,000,000  by  act  of  July  11,  1862;  $150,000,000 
authorized  by  acts  of  January  17  and  March  3,  1863. 
Besides  the  greenbacks  (issued  in  denominations  in  no 
case  under  a  dollar),  there  was  some  issue  of  fractional 
currency  and  of  interest-bearing  notes  running  for  a 
brief  period,  both  of  which  were  also  made  legal  tender.^ 
The  rise  in  prices  is  shown  by  the  following  table  :^ — 

1  Davis  Rich  Dewey,  Financial  History  of  the  United  States,  New 
York  (Longmans),  3d  ed.,  §  29. 

-  For  a  brief  account  of  the  greenbacks,  see  Dewey,  Financial 
History  of  the  United  States,  Chapter  XII.  The  most  complete 
account  is  found  in  Wesley  Clair  Mitchell,  A  History  of  the  Green- 
backs, Chicago  (University  of  Chicago  Press),  1903. 

*  Aldrich  Senate  Report  on  Wholesale  Prices  and  Wages,  52d 
Congress,  2d  Session,  table  24,  p.  93. 


Sec.  12] 


STATISTICAL   VERIFICATION 


259 


Index  Numbers  of  Prices  during  Greenback  Depreciation 


Price  op 

Index  Nos.  op  Northern  Prices  (1860  =  100) 

Yeab 

Gold' in 

Falkner^ 

Greenbacks 

In  Gold  3 

In  Paper  < 

Dun  6 
in  Paper 

Mitchell' 
Median 
in  Paper 

1861    .     . 

100 

94 

94 

89 

96 

1863    .     . 

144 

91 

132 

150 

134 

1865    .     . 

163 

107 

232 

169 

158 

1867    .     . 

138 

123 

166 

164 

150 

1869    .     . 

136 

112 

152 

143 

158 

1871    .     . 

112 

123 

136 

132 

130 

1873    .     . 

114 

115 

129 

124 

130 

1875    .     . 

115 

115 

129 

117 

121 

1877    .     . 

105 

107 

114 

95 

100 

1879    .     . 

100 

95 

95 

85 

85 

It  has  been  asserted  that  the  rise  of  prices  during  the 
greenback  depreciation  was  not  due  to  the  quantity 
of  the  greenbacks,  but  to  the  pubHc  distrust  of  green- 
backs. The  truth  is  probably  that  it  was  due  to  both. 
Distrust  was  evident  and  restricted  the  sphere  of 
greenbacks  very  materially.  California  and,  in  fact, 
all  the  region  west  of  the  Rocky  Mountains,  made 
strenuous  efforts  to  prevent  the  circulation  of  green- 
backs, —  efforts  which  were  largely  successful.  And 
naturally  the  greenbacks  could  not  circulate  in  the 
South.  These  restrictions  alone  would  confine  their 
circulation  to  a  population  of  about  20  millions  out  of  a 
total  population  in  1860  of  31  millions,  that  is,  to  less 

*  Average  of  quotations  in  January,  April,  July,  October,  from 
Wesley  Clair  Mitchell,  Gold  Prices  and  Wages  under  the  Greenback 
Standard,  Berkeley  (University  Press),  March,  1908. 

2  Weighted  arithmetical  average  of  articles  comprising  68.60  per 
<3ent  of  total  expenditure.        ^  Aldrich  Report,  p.  100.        *  Ibid.,  p.  93. 

*  From  Wesley  Clair  Mitchell,  ibid.,  p.  59. 


260 


THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 


than  two  thirds  of  the  entire  population.  Therefore 
the  volume  of  trade  for  which  the  greenbacks  were  used 
must  have  been  greatly  reduced.  The  total  circulating 
currency  during  the  war  is  not  known  with  certainty ; 
but  the  best  estimates  of  the  various  forms  of  circu- 
lating media  are  those  compiled  by  Mitchell.'  Though 
he  modestly  warns  the  reader  against  any  attempt  to 
cast  up  sums,  his  results  may  be  considered  as  at  least 
of  some  value.  The  totals,  omitting  money  in  the 
Treasury  and  interest-bearing  forms,  which  were  known 
to  have  only  a  very  sluggish  circulation,  we  find  to  be 
as  follows :  — 


Prices  op  all  Articles  aver- 

■1 

J. 

Roughly  estimated  Circula- 

aged 3    according  to  Impor- 

XtiiAJi 

tion  IN  Loyal  States  ^ 

tance,  comprising  68.60  %  op 

Total  Expenditure 

1860 

433 

100 

1861 

490 

94 

1862 

360 

104 

1863 

677 

132 

1864 

708 

172 

1865 

774 

232 

1866 

759 

188 

Considering  the  unreliability  of  the  figures  for  cur- 
rency ^  and  the  lack  of  data  as  to  the  other  magnitudes  in 
the  equation  of  exchange,  there  is  here  a  rough  corre- 
spondence between  the  volume  of  the  currency  and  the 
level  of  prices. 

1  Wesley  C.  Mitchell,  History  of  the  Greenbacks,  Cliicago  (Uni- 
versity of  Chicago  Press),  1903,  p.  179. 

2  Mitchell,  ibid.,  p.  179. 

^  Aldrich,  Report  on  Wholesale  Prices. 

*  The  great  reduction  in  1862,  for  instance,  is  due  to  the  assump- 
tion that  practically  all  gold  was  withdrawn  from  circulation  ex- 
cept in  California.  A  more  reasonable  assumption  would  seem  to 
be  that  it  was  only  partially  withdrawn.     Much  of  it  may  have 


Sec.  13]  STATISTICAL   VERIFICATION  261 

§13 

It  is  necessary  to  remember  that  the  confidence  with 
which  we  have  to  deal  is  not  primarily  confidence  in 
redemption,  but  confidence  in  the  paper  money, — its 
purchasing  power.  This  confidence  may  rest  on  ex- 
pectation of  redemption  or  on  other  conditions,  particu- 
larly the  expectation  of  further  inflation  or  contraction. 
The  explanation  of  the  value  of  the  greenbacks  appears 
to  me  to  be  in  brief  as  follows  :  — 

The  Redemption  Act  of  1875  announced  the  intention 
of  our  government  to  redeem  the  greenbacks  on  and  af- 
ter January  1,  1879.  Each  greenback  being  thus  kept 
equal  to  the  discounted  value  of  a  full  dollar  due  Jan- 
uary 1,  1879,  they  rose  steadily  toward  par  as  that  date 
approached.  Some  of  them  were  withdrawn  from  cir- 
culation to  be  held  for  the  rise.  The  value  of  a  green- 
back dollar  could  not  be  much  less  than  this  discounted 
value  of  the  gold  dollar  promised  in  1879;  otherwise 
speculators  might  withdraw  the  greenbacks  wholly. 
This  would  pay  them  well  provided  they  were  certain 
that  the  government's  promise  would  be  fulfilled.  On 
the  other  hand,  the  value  of  greenbacks  could  not,  with 
paper  money  redundant  for  trade,  be  greater  than  said 
discounted  value,  because  in  that  case  speculators 
would  return  it  all  to  the  circulation,  the  prospective 
rise  being  'Hoo  small  to  repay  the  interest"  lost  in 
carrying  it.  Thus  speculation  acted  as  a  regulator  of 
the  quantity  of  money. 

been  hoarded  in  coin  form  preparatory  to  export  or  melting.  If 
so,  it  probably  circulated  to  some  extent.  "Hoarding"  means  a 
longer  retention  in  the  same  hands,  but  not  necessarily  failure  to 
be  exchanged  at  all.  Gold  was  a  valuable  form  of  bank  "reserve" 
at  this  time.  While  not  paid  out  in  meeting  demand  obligations, 
it  was  a  very  quick  asset  and  could  be  quickly  realized  upon. 


262  THE    PURCHASING   POWER   OF  MONET       [Chap.  XI 

Thus  the  rise  in  value  of  the  greenbacks,  like  other  com- 
ing events,  cast  its  shadow  before.  It  was  ''discounted 
in  advance."  It  is  quite  true  that  confidence  in  redemp- 
tion was  here  the  ultimate  cause  of  the  appreciation  of 
the  paper  money;  but  the  readjustments  caused  by 
this  confidence  include  a  reduction  in  the  quantity  of 
the  money  in  circulation.  Without  such  readjustment 
the  appreciation  would  be  impossible,  as  the  equation  of 
exchange  plainly  shows.  We  should  note,  however,  that 
if  the  price  of  the  currency  were  already  sufficiently  high, 
the  prospect  of  future  redemption  would  not  further 
raise  it.  It  might  happen  that  the  value  of  the  currency 
was  already  above  the  discounted  par  value  promised 
at  the  time  set  for  redemption.  In  such  a  case  there 
need  not  be  any  speculation  or  any  immediate  rise  in 
value  until  the  date  of  redemption  drew  near  enough 
to  make  itself  felt.  On  the  other  hand,  when,  during 
the  war,  the  government  announced  a  further  issue  of 
a  paper  currency  already  depreciated,  the  public  antici- 
pated its  further  depreciation  by  releasing  such  hoards 
and  stocks  as  were  available ;  in  other  words,  by  accel- 
erating the  circulation  of  money.  Each  man  hastened 
to  spend  his  money  before  an  expected  rise  of  price, 
and  his  very  action  hastened  that  rise. 

Announcements  of  federal  defeats  in  the  war  acted 
in  the  same  way,  being  signals  that  further  issues  of 
greenbacks  might  be  required;  while  announcement 
of  victories  acted  in  the  opposite  way,  being  like  signals 
of  probable  redemption. 

When  appreciation  is  anticipated,  there  is  a  tendency 
among  owners  of  money  to  hoard  or  hold  it  back,  and, 
among  owners  of  goods,  to  sell  them  speedily ;  the  result 
being  to  decrease  prices  by  reducing  the  velocity  of  circu- 
lation and  increasing  the  volume  of  trade.    When,  on  the 


Sec.  141  STATISTICAL   VERIFICATION  263 

contrary,  depreciation  is  anticipated,  there  is  a  tendency 
among  owners  of  money  to  spend  it  speedily  and  among 
owners  of  goods  to  hold  them  for  a  rise,  the  result  being 
to  raise  prices  by  increasing  the  velocity  of  circulation 
and  decreasing  the  volume  of  trade.  In  other  words, 
the  expectation  of  a  future  rise  or  fall  of  prices  causes 
an  immediate  rise  or  fall  of  prices. 

These  anticipations  respond  so  promptly  to  every 
sign  or  rumor  that  superficial  observers  have  regarded 
the  rise  and  fall  of  the  greenbacks  as  related  directly 
and  solely  to  expected  redemption  and  as  having  no 
relation  to  quantity.  These  observers  overlook  the  real 
mechanism  at  work ;  they  fail  to  see  that  these  effects, 
though  quick,  are  slight  and  limited.  They  are  the 
simple  adjustments  of  transition  periods  described  in 
Chapter  IV.  It  would  be  a  grave  mistake  to  reason, 
because  the  losses  at  Chickamauga  caused  greenbacks 
to  fall  4  per  cent  in  a  single  day,  that  their  value  had 
no  relation  to  their  volume.  This  fall  indicated  a  slight 
acceleration  in  the  velocity  of  circulation,  and  a  slight 
retardation  in  the  volume  of  trade ;  but,  under  ordinary 
circumstances,  it  is  only  shghtly  that  the  velocity  of 
circulation  can  thus  be  accelerated;  while  to  make 
trade  stagnate  long  or  completely  would  require  a 
cataclysm. 

§  14 

In  the  South  it  is  ''impossible  to  state  even  approx- 
imately how  many  Confederate  treasury  notes  were 
outstanding  at  any  time."  ^  Professor  Schwab  has, 
however,  given  the  value  of  gold  in  Confederate  cur- 
rency and  index  numbers  of  prices  in  the  South.  He 
concludes :  ^  — 

'  J.  C.  Schwab,  Confederate  States  of  America,  1861-1865,  New 
York  (Scribner),  1901,  p.  165.  *  Ibid.,  pp.  167-169. 


264  THE   PURCHASING   POWER   OF   MONEY       [Chap.  XI 

"This  movement  of  the  gold  premium  corresponds 
roughly  with  the  amount  of  government  notes  out- 
standing in  each  period.  The  relatively  rapid  increase 
in  the  issue  of  notes  after  August,  1862,  during  the  last 
months  of  1863,  and  again  during  the  last  months  of 
the  war,  is  reflected  in  the  rapid  increase  of  the  gold 
premium  at  those  three  times.  When  the  amount  of 
outstanding  notes  remained  stationary  at  the  beginning 
of  1863,  there  was  a  somewhat  slower  advance  of  the 
gold  premium  during  those  months ;  while  the  shrink- 
ing of  the  outstanding  notes  during  the  first  half  of  1864 
is  distinctly  reflected  in  a  temporary  decline  of  the 
premium. 

"In  the  North  during  the  Civil  War  the  course  of  gold 
premium  only  remotely  suggested  the  amount  of  notes 
outstanding  at  any  time.  The  premium  rose  most 
rapidly,  or,  in  other  words,  the  notes  sank  in  value  most 
rapidly,  at  the  beginning  of  1863,  recovering  again 
during  the  second  quarter  of  that  year,  declining  after 
August,  1863,  to  their  lowest  point  in  the  summer  of 
1864,  and  rising  again  during  the  last  months  of  the 
war.^  The  value  of  the  'greenback'  was  much  more 
a  barometer  of  popular  feeling  as  to  the  eventual  out- 
come of  the  war  than  a  gauge  of  their  amount  in  cir- 
culation, for  the  latter  did  not  materially  increase  after 
July,  1863,  and  certainly  not  after  July,  1864.  In  fact, 
the  gold  value  of  the  federal  '  greenback '  ran  closely 
parallel  with  the  gold  value  of  the  federal  bonds  during 
the  war.  This  is  also  true  of  the  confederate  bonds  and 
treasury  notes.  These  two  sets  of  parallel  fluctuations 
were  evidently  caused  by  the  changing  credit  of  the  two 
governments  concerned. 

1  J.  C.  Schwab,  Confederate  States  of  America,  1861-1865,  Ne^V 
York  (Scribner),  1901,  table  on  p.  167. 


Sec.  15]  STATISTICAL   VERIFICATION  265 

"A  general  index  number  for  either  section,  based 
both  on  a  simple  and  a  weighted  average,  can  be  con- 
structed. The  hues  plotted  to  indicate  these  two  sets 
of  figures  do  not  run  parallel,  but  converge  and  diverge 
during  different  periods  of  the  war,  converging  at  those 
times  when  events  in  the  military,  the  political,  or  the 
financial  field  discouraged  the  South,  and  correspond- 
ingly encouraged  the  North  in  the  general  belief  that 
the  war  was  approaching  an  end ;  diverging  at  those 
times  when  federal  reverses,  or  similar  events  in  other 
than  the  military  field,  raised  the  hopes  of  the  South, 
and  led  to  behef  on  both  sides  that  the  war  would  be 
protracted."  ^ 

We  thus  see  that  redundancy  of  issue  produces  a 
rise  of  prices,  not  only  because  of  increased  quantity,  but 
because  of  decreased  confidence,^  which  affects  the 
sphere  of  use  of  the  money  and  therefore  the  volume 
of  trade  performed  by  the  money,  and  accelerates  its 
velocity. 

§  15 

We  have  given  historical  instances  of  the  effects  on 
prices  of  changes  in  the  precious  metals  and  in  paper 
money. 

There  remain  to  be  considered  historical  instances 
of  the  effects  on  prices  of  changes  in  deposit  currency. 
The  price  movements  due  to  changes  in  deposit  currency 
usually  include  those  culminations  called  crises  and  de- 
pressions. 

The  economic  history  of  the  last  century  has  been 

1  J.  C.  Schwab,  ibid.,  p.  179. 

2  Cf.  Wesley  Clair  Mitchell,  History  of  the  Greenbacks,  pp.  208  and 
210.  Also  Francis  A.  Walker,  Political  Economy,  3d  ed.,  New  York 
(Holt),  1888,  p.  164. 


266  THE    PURCHASING   POWER  OP  MONEY       [Chap.  XI 

characterized  by  a  succession  of  crises.  Juglar  in  his  de- 
scription of  the  conditions  preceding  crises  mentions  the 
signs  of  great  prosperity,  the  enterprise  and  the  specula- 
tion of  all  kinds,  the  rising  prices,  the  demand  for  labor, 
the  rising  wages,  the  ambition  to  become  at  once  rich, 
the  increasing  luxury,  and  the  excessive  expenditure.^ 

A  crisis  is,  as  Juglar  in  fact  defines  it,  an  arrest  of 
the  rise  of  prices.  At  higher  prices  than  those  already 
reached  purchasers  cannot  be  found.  Those  who  had 
purchased,  hoping  to  sell  again  for  profit,  cannot  dis- 
pose of  their  goods.- 

Our  previous  analysis  has  shown  us  that,  before  a 
crisis,  while  prices  are  ascending,  there  is  a  great  in- 
crease in  bank  deposits ;  and  that  these,  being  a  cir- 
culating medium,  accelerate  the  rise. 
fc  It  has  been  pointed  out  that,  with  trade  international, 
the  rise  of  prices,  resulting  from  expansion  of  deposits, 
is  also  international.  Even  if,  in  some  of  the  countries, 
deposits  should  not  expand,  a  rise  of  the  price  level 
would  nevertheless  occur.  The  expansion  of  deposits 
even  in  one  country  of  considerable  size  would,  by 
tending  to  raise  prices  there,  cause  the  export  of  gold. 
Thus,  in  other  countries  the  supply  of  money  would 
increase  and  prices  rise  also.  This  would  tend  to  stim- 
ulate expansion  of  deposits  in  these  other  countries  and 
bring  about  a  further  rise.     Even,  therefore,  if  credit 

1  Clement  Juglar,  Des  Crises  Commerciales  et  de  leur  Retour 
P6riodique  en  France,  en  Angleterre  et  aux  Etats-Unis,  2  ed.,  Paris 
(Guillaumin),  1889,  pp.  4  and  5.  See  also  translation  of  same  deal- 
ing with  United  States,  by  De  Courcy  W.  Thom,  A  Brief  History 
of  Panics  in  the  United  States,  New  York  (Putnam),  1893,  pp.  7-10. 
Juglar  is  mistaken  in  adding  that  interest  rates  fall  during  rising 
prices.  The  facts  show  that  they  rise,  though  not  sufficiently  to 
check  tke  excessive  lending.  See  Irving  Fisher,  The  Rate  of  Interestf 
Chapter  XIV. 

'  Juglar,  ibid.,  p.  14. 


Sec.  16] 


STATISTICAL   VERIFICATION 


267 


expansion  did  not  begin  at  the  same  time  in  all  the  prin- 
cipal commercial  countries,  the  beginning  of  it  in  one 
country  would  be  quickly  communicated  to  others. 
For  the  same  reason  the  arrest  of  rising  prices  and  the 
beginning  of  falling  prices  would  occur  at  about  the 
same  time  in  most  of  the  principal  countries.  As  a 
matter  of  fact  this  is  what  we  find  to  be  the  case.  Juglar 
has  made  out  a  table  showing  the  crises  in  England, 
France,  and  the  United  States  from  1800  to  1882.^ 
With  the  addition  of  the  dates  of  later  crises  the  table 
is  as  follows  :  — 


France 

England 

United  States 

1804 

1803 

1810 

1810 

1813-1814 

1815 

1814 

1818 

1818 

1818 

1825 

1825 

1826 

1830 

1830 

1836-1839 

1836-1839 

1837-1839 

1847 

1847 

1848 

1857 

1857 

1857 

1864 

1864-1866 

1864 

1873 

1873 

1873 

1882 

1882 

1884 

1889-1890 

1890-1891 

1890-1891 
1893 

1907 

1907 

1907 

§  16 

A  study  of  Juglar's  or  Thom's  tables  will  show  that, 
in  general,  bank  note  circulation  and  bank  deposit  cir- 
culation increase  before  a  crisis  and  reach  a  maximum 
at  the  time  of  the  crisis.  Index  numbers  of  prices  show 
the  same  general  trend. 

^  Juglar,  ibid.,  charts  at  end  ;  Thom's  translation,  p.  19,  brings  the 
table  to  1891. 


268  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

Thus,^  for  the  United  States,  the  crisis  of  1837-1839 
shows  that  circulation  of  state  banks  increased  each  year 
from  61  milHons  in  1830  to  149  in  1837  and  fell  to  116 
in  the  next  year ;  that  individual  deposits  rose  each  year 
from  55  miUions  in  1830  to  127  in  1837  and  fell  to  84  the 
next  year ;  that  from  1844  to  1848,  the  date  of  the  next 
crisis,  circulation  rose  from  75  millions  to  128,  falling 
back  to  114  the  next  year,  and  that  the  deposits  rose 
from  84  millions  to  103,  falling  back  to  91 ;  that  from 
1851  to  1857,  the  date  of  the  next  crisis,  circulation  rose 
from  155  millions  to  214,  falling  the  next  year  to  155,  and 
that  the  deposits  rose  from  128  millions  to  230,  falling 
the  next  year  to  185.  These  facts  —  that  prices  and  de- 
posits rose,  culminated,  and  fell  together  in  reference  to 
the  crises  of  1837,  1846,  and  1857  —  are  confirmed  by 
figures  for  per  capita  circulation  and  deposits  given  by 
Sumner.^  These  show  the  characteristic  sharp  check  to 
expansion  in  the  crisis  years,  mild  in  the  mild  crisis  of 
1846  and  pronounced  in  the  more  pronounced  crises  of 
1837  and  1857.  Corresponding  phenomena  occurred 
at  the  next  crisis,  1863-1864.  After  this  time,  the  chief 
statistics  are  for  national  banks,  and  these  show  simi- 
lar results.  Thus,  from  1868  to  1873,  national  bank 
circulation  rose  from  295  millions  to  341  and  then  fell, 
while  in  the  same  period  deposits  rose  from  532  mil- 
Uons  to  656  and  then  fell.  Similar,  though  less  marked, 
movements  occurred  in  the  milder  crises  of  1884  and 
1890,  which  is  the  last  included  in  Thom's  tables.  The 
crisis  of  1893  was  exceptional  and  largely  confined  to 
the  United  States,  being  chiefly  due  to  the  fear  as  to  the 

'  See  Thorn,  tables  following  p.  18. 

2  History  of  Banking  in  the  United  States,  Vol.  I  of  History  of  Bank- 
ing in  all  Nations,  New  York  (Journal  of  Commerce),  1896,  p.  456. 
The  figures  are  taken  from  37th  Congress,  3d  Session,  5  Ex.,  210. 


Sec.  16]  STATISTICAL   VEKIFICATION  269 

stability  of  the  gold  standard  without  much  reference 
to  currency  and  deposit  expansion.^  Whereas  in  the 
typical  speculative  cycle  the  ratio  of  deposits  to  re- 
serves gradually  increases  until  it  reaches  a  maximum 
just  before  the  crisis,  as  it  did  in  1873, 1884,  and  1907, 
this  did  not  happen  in  1893.  It  is  true  that  the  deposits 
of  national  banks  were  larger  in  1892  than  in  1890  or 
1891,  but  they  were  no  larger  relatively  to  reserves, 
though  possibly  this  fact  is  to  be  accounted  for  by  an  in- 
crease of  reserves  following  the  slight  crisis  of  1890-1891. 
It  is  true,  also,  that  the  ratio  of  the  deposits  of  national 
banks  to  reserves  was  high  in  1893,  but  this  was  due,  not 
to  an  expansion  of  deposits,  for  deposits  decreased  during 
that  year,  but  to  the  runs  on  the  banks  and  consequent 
depletion  of  their  reserves.^  The  crisis  of  1907,  on  the 
other  hand,  was,  like  that  of  1857,  typically  a  crisis  of 
currency  expansion.  The  facts  in  reference  to  this  crisis 
will  be  discussed  more  fully  in  the  following  chapter. 

In  France  the  same  tendency  of  circulation  and  de- 
posits to  reach  a  maximum  at  or  about  a  crisis  and  recede 
immediately  afterward  is  illustrated  fairly  well,^  es- 
pecially for  deposits. 

1  Lauck,  Causes  of  the  Panic  of  1893,  Boston  (Houghton,  Mifflin), 
1907,  p.  118.  O.  M.  W.  Sprague,  in  "History  of  Crises  under  the 
National  Banking  System,"  National  Monetary  Commission  Re-port, 
Senate  Document  538  (61st  Congress,  2d  Session),  points  out  that 
in  the  runs  on  banks  there  was  no  special  demand  for  gold,  and  is 
inclined  to  think  that  the  influence  of  the  currency  expansion  has 
been  exaggerated. 

^  For  a  statistical  comparison  of  this  with  typical  crises,  see 
article  by  Harry  G.  Brown,  "Typical  Commercial  Crises  versus  a 
Money  Panic,"  Yale  Review,  August,  1910. 

'  Juglar,  op.  cit.,  tables  following  p.  339  and  charts  at  end. 
Juglar  calls  the  crisis  of  1873  in  France  political  rather  than  com- 
mercial. The  statistics  of  circulation  and  deposits  and  their  velocity 
of  circulation  (as  shown  by  Pierre  des  Essars),  however,  reach  a 
maximum  in  1873  and  recede  immediately  after. 


270  THE    PURCHASING   POWER   OF  MONEY       [Chap.  XI 

For  the  Bank  of  England  we  find  the  same  general 
correspondence  between  crises,  circulation,  and  private 
deposits.^ 

§17 

Not  only  do  money  and  deposit  currency  {M  and  M') 
'rise  regularly  to  a  maximum  at  the  time  of  a  crisis,  but 
their  velocity  of  circulation,  so  far  as  statistics  indicate, 
goes  through  the  same  cycle.  Pierre  des  Essars  has 
demonstrated  this  beyond  peradventure,  so  far  as 
velocity  of  circulation  of  deposits  is  concerned.^ 

For  the  United  States  we  have  scarcely  any  statistics 
of  velocity  of  circulation  of  deposits,  but  those  for  two 
New  Haven  banks  and  for  an  Indianapolis  bank,  which 
I  have  secured  for  the  last  few  years,  show  a  maximum 
in  the  crisis  year  1907. 

After  a  crisis,  a  decrease  occurs  in  M,  M' ,  V,  and  F'. 
Bank  reserves  are  increased,  and  this  causes  a  decrease 
in  M. 

Since,  then,  currency  and  velocity  both  increase 
before  a  crisis,  reach  a  maximum  at  the  crisis,  and  fall 
after  the  crisis,  it  is  small  wonder  that  prices  follow  the 
same  course.  That  they  do  is  the  real  meaning  of  a 
crisis.  In  fact,  as  we  have  seen,  Juglar  defines  a  crisis 
as  an  arrest  of  a  rise  of  prices.  The  index  numbers  of 
prices  show  the  rise,  maximum,  and  slump  for  almost 
every  crisis  year  for  which  price  statistics  exist.^ 

*  Juglar,  op.  cit.,  tables  following  p.  291. 

2  "La  vitesse  de  la  circulation,"  Journal  de  la  Societe  de  Statistique 
de  Paris,  April,  1895,  p.  148.  From  1810  to  1892  in  France,  taking 
the  thirteen  crisis  years  and  the  twelve  years  of  "liquidation,"  Des 
Essars  finds  that,  unthout  exception,  the  velocity  of  circulation  of 
deposits  at  the  bank  of  France  is  a  maximum  in  the  crisis  years 
and  a  minimum  in  the  years  of  liquidation. 

^  The  detailed  figures  will  be  seen  in  the  Appendix  to  the  next 
chapter  (Chapter  XII). 


Sec.  17] 


STATISTICAL   VERIFICATION 


271 


The  following  figures  are  designed  to  present  a  picture 
of  the  crisis  of  1907  in  the  United  States  as  illustrating 
the  culmination  of  a  typical  credit  cycle:  — 


^  1 

C3 

03 

^ 

a 
o 

a 
o 

Is 

a 

o 

"o 

O  V 

Year 

2.2 
°3 

o  a 

a  § 

3 

1 

3"^ 

s 

a 

a^^ 

-  a  „ 

.s 

^a: 

'-''Eo 

z. 

Pirn 

.2.2  S 

C3 

t- 
^ 

5S 

OS 

f5><  0 

> 

1904    . 

3.31 

658 

5.0 

113 

228 

113.2 

.7 

4.2 

3.5 

1905   . 

3.78 

649 

5.8 

144 

279 

114.0 

5.3 

4.3 

-1.0 

1906   . 

4.06 

651 

6.2 

160 

315 

120.0 

6.6 

5.7 

-0.9 

1907   . 

4.32 

692 

6.2 

145 

323 

127.9 

-1.7 

6.4 

8.1 

1908   . 

4.38 

849 

5.1 

132 

294 

125.7 

4.4 

We  notice,  in  the  first  column,  a  steady  and  rapid  in- 
crease in  the  deposits  of  national  banks  up  to,  and  in- 
cluding, the  crisis  year.  Though  deposits  for  1908  do 
not  decrease,   yet  they  remain  almost  stationary  as 

1  The  figures  for  deposits  and  reserves  of  national  banks  are 
those  given  in  the  Reports  of  the  Comptroller  of  the  Currency,  and 
represent  the  condition  of  the  banks  at  their  third  report  to  the 
Comptroller  (generally  about  July  1)  of  each  year.  The  ratio 
column  explains  itself. 

2  The  figures  for  clearings  are  taken  from  the  Financial  Review 
for  1910,  p.  33.  Those  for  M'V  are  constructed  from  the  figures 
for  clearings  by  a  method  explained  in  §  5  of  Appendix  to  Chapter 
XII. 

'  The  index  numbers  of  prices  are  those  of  the  Bureau  of  Labor 
(Bulletin  81,  March,  1909),  and  relate  to  January  of  each  year  in 
question.  The  next  column,  therefore,  headed  "Per  cent  rise  of 
prices  during  year"  indicates  the  rise  from  January  of  the  year  in 
question  to  January  of  the  next. 

*  The  figures  for  interest  rates  are  taken  from  the  Appendix  of 
The  Rate  of  Interest,  p.  418,  brought  through  1908  by  computations 
from  the  Financial  Review.  The  per  cent  rise  of  prices  is  subtri"ted 
from  money  interest  to  get  virtual  interest. 


272  THE    PURCHASING   POWER   OF   MONEY       [Chap.  XI 

compared  with  those  of  the  previous  year.  The  second 
column,  that  for  reserves,  shows,  as  we  should  expect, 
a  large  increase  in  the  year  after  the  crisis,  the  banks 
having  fortified  themselves  against  the  decrease  of  busi- 
ness confidence.  We  find,  then  (third  column),  an  in- 
crease in  the  ratio  of  deposits  to  reserves,  the  highest 
ratio  being  reached  in  1906  and  1907,  not  because  re- 
serves were  depleted,  —  on  the  contrary,  they  were 
expanding,  —  but  because  deposits  were  expanding 
still  more  rapidly.  If  the  theory  presented  in  Chapter 
IV  is  correct,  it  is  precisely  this  high  ratio  of  deposits  to 
reserves,  brought  about  by  failure  of  interest  to  rise 
with  rise  of  prices,  which  forced  the  banks  to  raise  their 
rates  of  discount  and  so  check  further  expansion  of 
credit.  Then  came  the  crisis  and  the  short  succeeding 
depression.  The  next  column,  headed  "  clearings,"  is 
indicative  of  the  volume  of  check  transactions,  the  circu- 
lation of  deposit  currency.  As  a  fairly  constant  pro- 
portion of  checks  is  settled  through  the  various  clearing 
houses  of  the  country,  clearings  may  fairly  be  regarded 
as  somewhat  of  a  criterion  of  M'V.  The  fifth  column 
is  derived  from  the  fourth  and  from  other  data,  and 
is  intended  as  an  estimate  of  M'V.  These  two  col- 
umns increase  through  1906,  but  (since  they  relate  to 
the  whole  year  and  not  to  a  point  in  the  middle  of  the 
year)  begin  to  show  the  effects  of  the  credit  slump  in  the 
fall  of  1907,  so  that  their  growth  is  arrested  somewhat 
in  that  year,  and  still  more  in  the  year  after.  We 
should  expect  to  find,  then,  a  rise  of  prices  reaching  a 
maximum  with  1907  and  falhng  in  1908,  and  this  we  do 
find  in  column  six.  Column  seven  shows  the  per  cent 
rise  during  each  year.  Thus,  for  January,  1904,  the 
index  number  or  P  is  113.2,  and  for  January,  1905,  it 
is  114.0.     The  rise,  therefore,  is  a  little  less  than  1  per 


Sec.  17]  STATISTICAL   VERIFICATION  273 

cent.  The  minus  sign  signifies  a  fall.  The  eighth  col- 
umn is  for  rates  of  interest  and  indicates,  as  we  should 
expect,  a  rise,  culminating  in  1907.  Virtual  interest  — 
that  is,  the  interest  in  terms  of  commodities  —  was  ex- 
ceedingly low  during  the  years  immediately  preceding 
1907,  because  prices  were  rising  so  fast.  This  is  shown 
in  column  nine,  where  the  nominal  interest  (measured 
in  money)  is  corrected  by  the  rise  or  fall  of  prices  to 
give  interest  as  measured  in  actual  purchasing  power. 
With  the  culmination  of  the  cycle  in  1907  and  the  re- 
sultant fall  of  prices,  we  find  virtual  interest  suddenly 
becomes  very  high.  No  wonder  that  borrowing  enter- 
prisers often  found  it  hard  to  make  both  ends  meet. 

The  facts  as  to  credit  cycles,  then,  completely  con- 
firm the  analysis  already  given  in  previous  chapters 
and  indicate  that  prices  rise  and  fall  with  cycles  of 
currency  and  velocity.  For  the  benefit  of  those  who 
doubt  whether  the  expansion  of  deposit  currency  raises 
23rices,  or  whether  the  rise  of  prices  creates  deposit  cur- 
rency, it  may  be  added  that  facts,  as  well  as  theoiy, 
show  that  the  former  relationship  is  the  true  one  (al- 
though temporarily,  as  during  1904-1907,  there  exists 
a  reaction  of  prices  on  deposits).  Miss  England  has 
shown,  for  instance,  that  loans  and  deposits  expand  be- 
fore prices  rise,  and  that,  though  prices  often  fall  before 
loans  and  deposits  shrink,  this  anomalous  order  of 
events  is  explainable  by  the  revival  of  trade  following 
a  crisis.^ 

No  attempt  has  been  made  in  this  chapter  to  review 
all  the  phenomena  or  even  all  the  typical  phenomena 
of   crises.     We   are   not    here    concerned   with    crises 

1  Minnie  Throop  England,  "  Statistical  Inquiry  into  the  Influence 
of  Credit  upon  the  Level  of  Prices,"  University  Studies  (University 
of  Nebraska),  1907. 

T 


274  THE   PURCHASING    POWER   OF  MONEY      [Chap.  XI 

except  in  relation  to  currency.  Our  concern  is  with 
the  magnitudes  entering  the  equation  of  exchange,  es- 
pecially M,  M',  and  V\  for  these  are  the  immediate 
elements  the  variations  in  which  affect  the  price  level 
and  cause  it  to  rise  and  fall. 

§18 

This  chapter  has  been  devoted  to  an  historical  study 
of  changes  in  the  quantity  of  currency  and  of  the  effects 
of  these  changes  on  prices.  We  have  seen  that,  on  the 
whole,  increases  in  the  amount  of  money  have  tended 
to  raise  prices  from  century  to  century  during  the  last 
thousand  years,  and  especially  since  the  discovery  of 
America.  The  changes  in  the  last  century,  or  more 
exactly,  from  1789  to  1909,  have  been  considered  in 
somewhat  more  detail,  covering  five  periods  of  alter- 
nately rising  and  falling  prices.  We  have  seen  evidence 
to  connect  these  price  movements  with  changes  in  the 
quantity  of  money  and  in  the  volume  of  business.  The 
periods  1789-1809,  1849-1873,  and  1896-1909  were 
periods  of  rising  prices  and  large  increases  of  the  money 
supply.  In  the  period  1809-1849  prices  fell  presumably 
because  of  a  falling  off  in  gold  and  silver  production  and 
a  continuing  increase  of  business ;  while  between  1873 
and  1896,  although  the  world's  stock  of  precious  metals 
was  increasing  slowly,  prices  in  gold  countries  fell, 
because  in  addition  to  the  increasing  volume  of  business 
there  was  a  stampede  of  nations  to  adopt  the  gold  stand- 
ard and  demonetize  or  limit  the  coinage  of  silver. 

We  have  observed  the  recent  continual  increase  of 
gold  production  and  found  reasons  for  the  tentative 
prediction  that  the  gold  production  of  the  future  would 
continue  excessive  and  probably  cause  the  present  rise 
of  prices  to  continue  for  some  time  in  the  future. 


Sec.  18]  STATISTICAL   VERIFICATION  275 

We  have  described  some  of  the  chief  examples  of  paper 
money  inflation  and  shown  that  the  records  for  circula- 
tion and  price  changes  bear  out  in  a  general  way  the 
principles  set  forth  in  previous  chapters.  The  paper 
money  experiences  of  France  during  the  French  Revolu- 
tion, of  England  during  the  Napoleonic  wars,  of  Austria, 
the  American  colonies,  the  United  States,  and  the  Con- 
federacy have  been  briefly  reviewed.  We  have  noted 
that  in  these  cases,  as  in  others,  prices  depended  on  the 
quantity  of  money,  its  velocity,  and  the  volume  of  busi- 
ness. We  have  seen  that  the  apparent  exceptions 
due  to  lack  of  confidence  in  paper  money  are  not 
really  exceptions,  because  lack  of  confidence  works  it- 
self out  through  the  magnitudes  in  the  equation  of  ex- 
change. Distrust  increases  the  velocity  of  circulation, 
and  decreases  the  trade  performed  by  the  money.  We 
have  shown  that  the  general  effect  of  irredeemable  paper 
money  issues,  which  are  almost  always  in  large  quanti- 
ties, despite  pledges  to  the  contrary,  has  been  to  raise 
prices. 

Finally,  our  study  of  deposit  circulation  and  crises 
has  afforded  further  illustration.  Preceding  a  typical 
crisis,  there  is,  in  general,  a  tendency  for  deposits  to 
increase  and  also  for  their  velocity  of  circulation  to  in- 
crease, while  prices  tend  to  rise.  Following  the  crisis 
comes  a  decrease  in  bank  deposits  and  their  velocity  of 
circulation,  an  increase  in  bank  reserves,  with  a  corre- 
sponding tendency  to  diminish  money  in  circulation,  and 
a  fall  of  prices.  In  the  years  of  the  principal  crises 
these  took  place  simultaneously  in  different  countries. 


CHAPTER  XII 

STATISTICS    OF    RECENT    YEARS 
§1 

The  last  chapter  was  devoted  to  a  brief  sketch  of  price 
movements  and  their  causes,  in  so  far  as  the  scanty  data 
available  make  even  a  tentative  interpretation  possible. 
From  this  telescopic  view  of  the  past  we  turn  to  a  micro- 
scopic view  of  the  present.  We  shall  confine  it  to  a 
study  of  the  events  of  the  last  three  decades  in  the 
United  States.  In  the  study  of  the  last  chapter  we 
found  the  facts  of  history  to  be  in  accord  with  the  a 
priori  principles  already  set  forth  in  the  equation  of 
exchange.  But  these  facts  of  history  were  too  general 
and  vague  to  constitute  a  quantitative  fulfillment  of  the 
equation  of  exchange.  We  shall  find,  however,  much 
fuller  data  in  the  last  few  decades.  We  shall  see  that 
the  equation  of  exchange,  which  has  already  been 
proved  a  priori,  may  also  be  verified  by  actual  statistics 
—  within  at  least  the  limit  of  error  to  which  the  statis- 
tics are  liable. 

A  good  beginning  of  such  a  study  is  afforded  by  the 
pioneer  work  of  Professor  Kemmerer,  already  often  re- 
ferred to.  He  has  estimated  ^  roughly  the  chief  magni- 
tudes of  the  equation  of  exchange  and  found  that  these 
conform  in  a  general  way  to  the  conditions  which  the 
equation  of  exchange  imposes.     For  each  year,  begin- 

^  Money  and  Credit  Instruments  in  their  Relation  to  General  Prices, 
New  York  (Holt),  1909,  Book  II. 

276 


Sec.  1]  STATISTICS  OF  RECENT  YEARS  277 

ning  with  1879  (the  year  of  resumption  of  the  gold  stand- 
ard), and  ending  with  1908,  he  has  estimated  the  total 
monetary  and  check  circulation  (what  we  have  called 
MV  and  M'V)  and  the  volume  of  trade  {T),  and  from 
these  has  calculated  ^  what  the  price  level  ought  to 

be  as  determined  by  these  factors,  i.e.     — ■. — ^ 

This  calculated  magnitude,  which  Professor  Kemmerer 
calls  the  "  relative  circulation  of  money,"  he  then  com- 
pares with  the  actual  figures  for  price  levels  as  given  in 
statistics  of  index  numbers. 

Professor  Kemmerer's  calculation  is,  I  believe,  the 
first  serious  attempt  ever  made  to  test  statistically  the 
so-called  "  quantity  theory  "  of  money.  The  results 
show  a  correspondence  which  is  very  surprising  when 
we  consider  the  exceedingly  rough  and  fragmentary 
character  of  the  data  employed. 

Most  other  writers  who  have  attempted  to  test  the 
quantity  theory  statistically  seem  to  have  been  ani- 
mated by  a  desire  not  to  give  it  a  fair  test,  but  to 
disprove  it.  They  have  carefully  avoided  taking  ac- 
count of  any  factors  except  money  and  prices.  It  is 
not  to  be  wondered  at  that  they  find  little  statistical 
correlation  between  these  two  factors.^  The  virtue 
of  Professor  Kemmerer's  work  consists  in  giving  due 
attention  to  factors  other  than  money. 

The  chief  error  in  his  investigation  is  the  assumption 
of  47  as  the  velocity  of  circulation  of  money.  The  true 
value,  as  we  shall  see,  is  nearer  18  to  20.    But  the  volume 

1  For  the  details  of  Professor  Kemmerer's  calculations  the  reader 
is  referred  to  his  book.  A  very  brief  summary  and  criticism  are 
given  in  §  1  of  the  Appendix  to  (this)  Chapter  XII. 

^  See  e.g.  Miss  S.  M.  Hardy,  "The  Quantity  of  Money  and 
Prices,  1860-1891.  An  Inductive  Study."  Journal  of  Political 
Economy,  Vol.  3,  pp.  145-168. 


278        THE    PURCHASING   POWER   OF  MONEY        [Chap.  XII 

of  money  payments,  even  with  Kemmerer's  exaggerated 
figure  for  velocity,  is  so  small  when  compared  with 
check  payments,  that  this  weakness  does  not  greatly 
affect  his  final  comparisons.  At  my  request,  Professor 
Kemmerer  has  recalculated  his  curves  on  the  basis  of 
18  instead  of  47  as  the  velocity  of  circulation  of  money. 
The  results  are  given  in  Fig.  12.  If  these  are  com- 
pared with  those  contained  in  Professor  Kemmerer's 
book,  there  will  be  seen  to  be  little  difference.  It  is 
interesting  to  observe  that  when  minute  comparison  is 


Fig.  12. 

made  the  selection  of  18  as  the  estimate  of  velocity 
gives  a  slightly  better  agreement  between  the  two 
curves  than  does  47. 

The  ''coefficient  of  correlation"  between  Professor 
Kemmerer's  results  for  P,  as  directly  shown  by  statis- 
tics and  as  indirectly  calculated  from  the  other  factors 
in  the  equation  of  exchange,  is  found,  by  Professor 
Persons  ^  of  Dartmouth,  to  be  only  .23  (or  23  per  cent 
of  perfect  correlation),  with  a  probable  error  of  .13. 
As  Professor  Persons  says,  this  is  a  very  low  degree  of 
correlation. 

'  "  Quantity  Theory  as  tested  by  Kemmerer,"  Quarterly  Journal 
of  Economics,  February,  1908,  p.  287. 


Sec.  1]  STATISTICS   OF  RECENT  YEARS  279 

But  Persons's  method  of  testing  agreement  by  means 
of  a  coefficient  of  correlation  is  not  really  applicable  to 
two  curves  representing  magnitudes  changing  in  time. 
For  it  practically  ignores  a  most  essential  factor,  their 
order  in  time.  A  year-to-year  comparison  is  better. 
If  we  consider  the  curves  of  prices  and  of  ''relative  cir- 
culation," ^  we  see  at  a  glance  that  almost  every  succes- 
sive change  in  direction  in  the  one  curve  is  matched  by  a 
corresponding  change  in  direction  in  the  other.  In  fact, 
out  of  28  such  possible  coincidences,  we  find  the  actual 
number  to  be  16  cases  of  agreement  in  the  changes  of 
direction,  9  cases  of  disagreement,  and  3  cases  of  a 
neutral  kind  {i.e.  cases  which  showed  no  change  of 
direction  in  one  of  the  two  curves). 

The  above  figures  relate  to  the  curves  in  Professor 
Kemmerer's  book.  The  later  curves  employing  18 
instead  of  47  for  money-velocity  show  about  the  same 
results,  there  being  16  cases  of  agreement,  8  cases  of  dis- 
agreement, and  4  cases  of  a  neutral  kind.  The  corre- 
spondence here  between  prices  and  "relative  circulation" 
is  very  slightly  greater  than  before.  In  both  sets  of  dia- 
grams the  agreements  are  not  only  much  more  numerous 
but  much  more  pronounced  than  the  disagreements. 

Finally,  some  of  the  disagreements  seem  to  be  really 
agreements,  disguised  by  being  shifted  forward  one  year. 
Thus,  the  inflections  of  1899,  1900,  1901,  for  "  relative 
circulation,"  although  all  counted  as  cases  of  disagree- 
ment, are  strikingly  similar  respectively  to  the  inflec- 
tions of  1900,  1901,  1902,  for  "general  prices."  From 
the  fact  that  the  statistics  are  partly  for  calendar  and 
partly  for  fiscal  years,  such  one-year  shifting  of  corre- 
spondence is  to  be  expected,  as  Professor  Kemmerer 
points  out. 

1  Kemmerer,  op.  cit.,  p.  149. 


280        THE    PURCHASING   POWER  OF  MONEY         [Chap.  XII 

§2 

I  shall  now  attempt  to  make  as  precise  statistical 
estimates  of  the  magnitudes  in  the  equation  of  exchange 
for  the  years  1896-1909  as  the  data  available  will  allow. 
This  period  —  1896-1909  —  is  selected  chiefly  because 
its  two  end  years  afford  the  only  known  data  making 
possible  an  estimate  of  velocity  of  circulation  of  money 
and  of  bank  deposits. 

The  magnitudes  will  be  considered  in  the  order 
M,  M',  V,  V,  T,  P.  For  each  the  figures  to  be  used 
are  new. 

M.  The  following  table  gives  the  estimated  amount  of 
money  in  circulation  in  the  United  States.  By  this 
we  mean  the  total  amount  of  money  (coin  and  paper) 
outside  of  the  federal  treasury  and  outside  the  banks 
of  deposit  and  discount  (national,  state,  private  and 
trust  companies).  The  treasury  stock  is  excluded  be- 
cause it  is  a  hoard  which  does  not  become  adjusted 
to  needs  of  payment  in  the  sense  —  or  at  any  rate  in  the 
degree  —  that  the  stocks  in  merchants'  tills  and  in 
people's  pockets  become  adjusted.  The  bank  reserves 
are  excluded  because,  as  we  have  shown,  they  are  used 
for  banking  operations,  not  commercial  purchases. 


Estimated  Money  in  Circulation  in  the  United  States  (M) 
(in  Billions  of  Dollars) 


1896 

1897 
1898 
1899 
1900 
1901 
1902 


.87 
.88 
.96 
1.03 
1.17 
1.22 
1.26 


1903 
1904 
1905 
1906 
1907 
1908 
1909 


1.38 
1.37 
1.45 
1.59 
1.63 
1.63 
1.63 


This  table  is  based  on  the  oflScial  estimate  of  money 
in  the  United  States,  which  includes  money  in  banks  and 


Sec.  2]  STATISTICS  OF  RECENT  YEARS  281 

in  the  federal  treasury.  These  official  figures  are  then 
corrected  by  means  of  recent  revisions  of  the  estimates 
of  the  gold  in  the  United  States,  and  by  deducting  the 
money  in  the  federal  treasury  and  the  estimate  of  money 
in  banks  reporting  and  unreporting.^  The  results  differ 
somewhat  from  the  official  figures  for  so-called  "money 
in  circulation,"  the  chief  reason  for  the  discrepancy  being 
that  these  official  figures  include  money  in  banks.  The 
figures  here  given  are  probably  nearly  correct ;  the  prob- 
able error  may,  I  believe,  be  assumed  to  be  within  2  or 
3  per  cent. 

The  table  shows  that,  during  the  space  of  thirteen 
years  between  1896  and  1909,  the  money  in  circulation 
has  nearly  doubled  and  that  its  increase  has  been  almost 
uninterrupted. 

M'.  The  following  figures  for  M'  are  estimates  of 
individual  deposits,  subject  to  check. 

Individual  Deposits  subject  to  Check  (M')  "^  (in  Billions  of 
Dollars) 


1896 2.68 

1897 2.80 

1898 3.19 

1899 3.90 

1900 4.40 

1901 5.13 

1902 5.43 


1903  5.70 

1904  5.80 

1905  6.54 

1906  6.84 

1907  7.13 

1908  6.60 

1909  6.75 


These  figures  are  based  on  the  official  figures  for  'in- 
dividual deposits,"  but  are  much  less  than  these,  owing 
to  the  fact  that  the  official  figures  include  deposits  in 
savings  banks  and  other  deposits  not  subject  to  check, 
as  well  as  to  several  other  minor  causes.  The  estimates 
here  given  constitute  the  first  attempt  to  give  a  series 

^  For  details  as  to  the  construction  of  the  table,  see  §  2  of  Ap- 
pendix to  (this)  Chapter  XII. 

2  For  the  method  of  estimating  these  figures  see  §  3  of  Appendix 
to  (this)  Chapter  XII. 


282        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 

of  figures  for  the  bank  deposits  subject  to  check  in  the 
United  States.  It  was  made  possible  through  the  kind 
cooperation  of  the  National  Monetary  Commission 
and  its  expert,  Mr.  A.  Piatt  Andrew.^ 

These  figures  give,  therefore,  the  actual  deposit  cur- 
rency of  the  United  States.  They  show  an  enormous 
growth  of  bank  deposit  currency.  In  the  space  of 
thirteen  years  (between  the  beginning  and  the  end  of  the 
table)  it  has  nearly  trebled.  Moreover,  each  year  shows 
an  advance  over  the  preceding  year,  excepting  only  the 
year  1908  following  the  crisis  of  1907. 

§3 

Having  found  M  and  M',  the  circulating  media,  we 
next  proceed  to  ascertain  V  and  V,  their  velocity  of  cir- 
culation. We  shall  find  it  convenient  to  consider  the 
latter  first. 

The  velocity  of  circulation  of  bank  deposits  is  found 
by  dividing  respectively  the  total  check  circulation 
(M'V)  by  the  bank  deposits  (M').  The  divisor,  M', 
has  already  been  found.  As  to  the  dividend,  M'V,  this 
is  practically  the  total  checks  drawn  in  a  year,  for  we 
may  reasonably  assume  that,  on  the  average,  each  check 
circulates  against  goods  once  and  but  once.^ 

For  two  years,  1896  and  1909,  thanks  to  the  efforts  of 
Professor  Kinley  of  the  University  of  IlHnois,  we  have 
voluminous  and  unique  data  collected  originally  for  the 
purpose  of  calculating  the  ratio  of  money-transactions 
to  check-transactions  in  the  United  States,  i.e.  the  ratio 
of  MV  to  M'V.  We  shall  see  that  these  data,  in  con- 
junction with  other  oflficial  statistics,  are  sufiicient  for 
something  more  important  than  computing  this  ratio ; 

1  For  details  see  §  3  of  Appendix  to  (this)  Chapter  XII. 
*  Cf.  Kem merer,  op.  cit.,  p.  114. 


Sec.  3]  STATISTICS   OF  RECENT   YEARS  283 

for  they  enable  us  to  calculate  with  a  tolerable  degree 
of  exactness  the  magnitudes  V  andF'  for  both  the  years 
mentioned.  We  shall  find  incidentally  that,  with  the 
aid  of  these  magnitudes,  it  is  possible  to  work  out  more 
exactly  than  in  the  investigations  above  mentioned  the 
very  magnitude  for  which  these  investigations  were 
undertaken,  viz.  the  ratio  of  money-transactions  to 
credit-transactions. 

We  need  first  to  estimate  M'V. 

M'V.  Professor  Kinley's  special  investigation  of 
1896  indicates  that  on  ''the  settling  day  nearest  July  1, 
1896,"  the  value  of  the  checks  deposited  was  about 
$468,000,000.  If  we  could  assume  that  this  day  was  an 
average  day  for  the  year,  we  should  need,  in  order  to 
obtain  the  total  year's  deposits  of  checks,  simply  to 
multiply  this  by  the  number  of  settling  days  in  1896, 
which  was  305.^  But  it  happens  that  July  1  is  an  excep- 
tionally heavy  day  in  the  deposit  of  checks.  Making 
allowance  for  this  fact,  2£>  indicated  by  the  clearings  of 
the  New  York  clearing  house,  we  conclude  that  the 
total  year's  deposits  of  checks  in  1896  was  about  97  bil- 
lions, with  a  probable  error  of  some  5  or  6  per  cent.^ 
Similar  calculations  for  1909  make  the  total  check  trans- 
actions of  that  year  364  billions.^  We  have  thus  the 
value  of  the  total  check  circulation  {M'V)  in  the  two 
years  1896  and  1909,  and  find  them  to  be  97  and  364 
billions  respectively,  indicating  a  prodigious  growth  in 
thirteen  years.  We  have  still  to  interpolate  figures  for 
intervening  years.  For  the  period  between  these  two 
years,  we  have,  unfortunately,  no  such  data  as  those  of 

»  This  multiplication  gives  $143,000,000,000,  which  figure  is  used 
by  Professor  Kemmerer  {op.  cit.,  pp.  110-111). 

*  The  method  of  reaching  this  result  is  described  in  §  4  of  Appen- 
dix to  (this)  Chapter  XII. 

»  See  §  4  of  Appendix  to  (this)  Chapter  XII. 


284        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XH 

Professor  Kinley  for  1896  and  1909.  However,  we  can 
find  an  excellent  barometer  in  the  clearing  house  trans- 
actions, —  a  barometer  dependent  partly  on  the  clearings 
in  New  York  City,  but  more  on  those  outside  of  New 
York  City.  It  is  well  recognized  that,  although  the 
clearings  in  New  York  deserve  an  exceedingly  large 
representation,  their  relative  importance  in  the  total 
clearings  is  exaggerated.^ 

On  the  question,  therefore,  ''What  relative  impor- 
tance should  be  given  respectively  to  clearings  in  New 
York  and  to  the  outside  clearings  in  order  to  get  the  best 
barometer  of  the  check  transactions  for  the  entire  coun- 
try?" we  conclude  that,  if  the  out-lde  clearings  be 
multiplied  by  five  and  the  result  added  to  the  New  York 
clearings,  we  shall  have  a  good  barometer  of  check 
transactions  for  the  United  States.- 
I  By  means  of  this  barometer  of  check  transactions, 
consisting  of  New  York  clearings  plus  five  times  the  out- 
side clearings,  and  our  knowledge  of  the  actual  check 
transactions  of  1896  and  1909,  we  may  easily  derive 
from  the  "barometer"  an  estimate  of  the  actual  check 
transactions.     The  result  is  as  follows  :  — 


Estimated  Check  Transactions  (M'V)  (in  Billions  of 
Dollars)  1896-1909' 


1896 
1897 
1898 
1899 
1900 
1901 
1902 


97 
106 
127 
166 
165 
208 
222 


1903 
1904 
1905 
1906 
1907 
1908 
1909 


223 

233 
282 
320 
320 
300 
364 


*  See  e.g.  the  remarks  on  these  clearings  in  Financial  Review  for 
1910,  p.  33,  and  in  Babson's  Business  Barometers  (Wellesley  Hills, 
Mass.),   1910,  p.   188. 

*  See  §  5  of  Appendix  to  (this)  Chapter  XII. 
'  See  §  5  of  Appendix  to  (this)  Chapter  XII. 


Sec.  4] 


STATISTICS   OF   RECENT   YEARS 


285 


The  probable  error  of  the  figures  between  1896  and  1909 
may  be  set  at  some  5  to  10  per  cent. 

F'.  Having  obtained  estimates  of  M'V  and  having 
previously  obtained  estimates  of  M',  it  is  easy,  by  simple 
division,  to  obtain  F'.     The  results  are  as  follows  :  — 

Estimated  Velocity  (F')  of  Circulation,  by  Checks,  of  De- 
posits Subject  to  Check 


1896 
1897 
1898 
1899 
1900 
1901 
1902 


36 

1903 

38 

1904 

40 

1905 

43 

1906 

37 

1907 

41 

1908 

41 

1909 

39 
40 
43 
47 
45 
46 
54 


The  probable  error  in  these  figures  may  be  set  at  some  5 
to  10  per  cent,  being  least  for  1896  and  1909  and  greatest 
midway  between.    , 

We  note  that  the  velocity  of  circulation  has  increased 
50  per  cent  in  thirteen  years  and  that  it  has  been  sub- 
ject to  great  variations  from  year  to  year.  In  1899  and 
1906  it  reached  maxima,  immediately  preceding  crises. 
These  results  correspond  to  those  of  Pierre  des  Essars 
for  the  rates  of  turnover  of  deposits  in  continental 
banks  already  noted,  except  that  he  usually  finds  the 
maximum  in  the  crisis  year  itself  rather  than  the  year 
before.  It  is  to  be  noted  that  the  figure  for  1909  is 
much  the  highest  in  the  table.  Whether  it  portends  an 
approaching  crisis,  time  will  determine. 


§4 

MV.  Our  next  quest  is  for  the  velocity  of  circula- 
tion of  money.  The  calculation  of  the  velocity  of  circu- 
lation of  money  presents  great  difficulties,  —  difficulties 
which,  in  fact,  have  usually  been  considered  insurmount- 


286         THE   PURCHASING   POWER   OF  MONEY        [Chap.  XII 

able.     This  opinion  was  well    expressed  by  Jevons/ 
who  wrote : 

"  I  have  never  met  with  any  attempt  to  determine  in  any  coun- 
try the  average  rapidity  of  circulation,  nor  have  I  been  able  to 
think  of  any  means  whatever  of  approaching  the  investigation  of 
the  question,  except  in  the  inverse  way.  If  we  know  the  amount  of 
exchanges  effected,  and  the  quantity  of  currency  used,  we  might 
get  by  division  the  average  number  of  times  the  currency  is  turned 
over;  but  the  data,  as  already  stated,  are  quite  wanting." 

As  we  shall  see,  however,  data  now  exist,  capable  of 
revealing  the  ''amount  of  exchanges  effected,"  or,  MV. 
In  fact,  this  is  equal  to  the  total  money  deposited 
in  banks,  plus  the  total  money-wages  paid,  plus  a  small 
miscellaneous  item.  From  MV  and  M  it  is  of  course 
easy  to  obtain  V  by  division. 

The  formula  for  obtaining  MV  is  as  simple  as  it  may 
at  first  seem  mysterious.  The  chief  peculiarity  of  the 
method  which  this  formula  represents,  and  the  feature 
which  adapts  it  to  practical  use,  is  that  it  utilizes  bank 
records  and  other  ascertainable  statistics  as  a  means  of 
discovering  the  total  value  of  money  transactions.  The 
method  is  based  on  the  idea  that  money  in  circulation 
and  money  in  banks  are  not  two  independent  reservoirs, 
but  are  constantly  flowing  from  one  into  the  other,  and 
that  the  entrance  and  exit  of  money  at  banks,  being  a 
matter  of  record,  may  be  made  to  reveal  its  circulation 
outside. 

It  is  obvious  how  the  bank-record  would  be  read,  were 
it  true  that  every  dollar  withdrawn  from  banks  cir- 
culated once  and  only  once  before  being  redeposited. 
Under  these  circumstances  the  annual  flow  of  monetary 
circulation  would  exactly  equal  the  annual  withdrawal 

'  Money  and  the  'Mechanism  of  Exchange  (London),  p.  336. 


Sec.  4]  STATISTICS  OF  RECENT  YEARS  287 

from  banks  prior  to  circulation,  as  well  as  the  annual 
deposits  in  banks  subsequent  to  circulation. 

Since  we  have  a  record  of  the  first  and  last  steps  of 
the  three,  viz.  the  withdrawals  and  the  deposits,  we 
possess  the  means  of  knowing  the  intermediate  step, 
the  exchange  of  money  for  goods.  The  ordinary  circula- 
tion of  money,  —  excluding  cases  where  it  changes 
hands  more  than  once  between  withdrawal  and  rede- 
posit,  —  is  equal  to  the  money-flow  through  banks. 

The  complete  facts,  however,  are  not  so  simple,  for 
the  reason  that  money  withdrawn  from  banks  is  often 
circulated  more  than  once.  Yet  the  complications 
involved  follow  definite  laws.  They  do  not  destroy  the 
value  of  the  bank  record,  but  merely  make  it  somewhat 
more  difficult  to  read.  We  propose  to  show  (1)  that  in 
actual  fact  much  money  circulates  out  of  bank  only  once, 
as  in  the  hypothetical  case  just  mentioned;  (2)  that  when 
it  is  paid  for  wages,  it  usually  circulates  twice ;  and  (3) 
that  only  rarely  does  it  circulate  three  or  more  times 
before  completing  its  circuit  back  to  the  banks. 

This  statement  means  that,  like  checks,  money  circu- 
lates in  general  only  once  outside  of  banks;  but  that 
when  it  passes  through  the  hands  of  non-depositors 
(which  practically  means  wage-earners)  it  circulates 
once  more,  thus  adding  the  volume  of  wage  payments  to 
the  volume  of  ordinary  money  circulation,  which,  as  we 
have  seen,  is  equal  to  the  flow  of  money  through  banks. 

We  falsely  picture  the  circulation  of  money  in  modern 
society  when  we  allow  ourselves  to  think  of  it  as  consist- 
ing of  a  perpetual  succession  of  transfers  from  person  to 
person.  Were  it  such  a  succession,  it  would  be,  as  Jevons 
said,  beyond  the  reach  of  statistics.  But  we  may 
form  a  truer  picture  by  thinking  of  banks  as  the  home 
of  money,  and  the  circulation  of  money  as  a  temporary 


288         THE    PURCHASING   POWER  OP  MONEY        [Chap.  XII 

excursion  from  that  home.  If  this  description  be  true, 
the  circulation  of  money  is  not  very  different  from  the 
circulation  of  checks.  Each  performs  one  transaction 
or,  at  most,  a  few  transactions,  outside  of  the  bank,  and 
then  returns  home  to  report  its  circuit. 

As  is  shown  in  the  Appendix,  the  total  money  de- 
posited in  banks  in  1896  amounted  to  nearly  10  billions  of 
dollars,^  and  the  total  expenditures  of  non-depositors 
to  nearly  6  billions,  of  which  4|  bilUons  constituted 
the  expenditures  of  wage-earners ;  the  remaining  item 
in  the  formula  for  circulation  amounted  to  less  than 
1  biUion,  making  about  16  billions  for  the  total  cir- 
culation. 

For  1909  the  corresponding  figures  are:  money  de- 
posited, 21  billions;  expenditures  of  non-depositors,  13 
billions;  and  the  remaining  item  about  1  billion,  making 
35  billions  in  all. 

The  following  table  summarizes  these  results  in  bil- 
lions of  dollars :  ^  — 


1896 

1909 

1st  term  (money  deposited  in  banks)      .     .     . 
2d  term  (expenditure  of  "  non-depositors  ")    . 
Remaining  item 

10- 
6- 
1- 

16  + 

21 

13 

1 

Total    

35 

'  For  a  fuller  account  of  the  method  of  estimating  the  velocity 
of  circulation  of  money  and  its  statistical  application,  see  §  6  of  the 
Appendix  to  (this)  Chapter  XII,  which  consists,  with  revisions  and 
additions,  of  an  article  of  mine  published  in  December,  1909,  in 
the  Journal  of  the  Royal  Statistical  Society  on  "A  New  Method  of 
estimating  the  Velocity  of  Circulation  of  Money."  The  additions 
incorporated  in  the  Appendix  (§§  7,  8)  include  the  statistical  de- 
tails of  the  calculations  for  the  United  States. 

'  For  details  as  to  the  figures  in  this  table,  see  §  7  of  Appendix 
to  (this)  Chapter  XII. 


Sec.  4]  STATISTICS  OF  RECENT  YEARS  289 

V.  In  order  to  obtain  the  velocity  of  circulation,  the 
total  circulation,  MV  (16  billions  for  1896,  or  to  be  more 
exact,  16.2  billions),  must  be  divided  by  the  amount  of 
money,  M,  circulating  in  1896.  This  amount  is  estimated 
at  $870,000,000.  Hence  the  velocity  is  16,200,000,000  -4- 
870,000,000  =  18.6,  or  about  19  tunes  a  year.  In  other 
words,  money  was  held  on  the  average  about  365  -^  19, 
which  amounts  to  19  or  20  days.  If  I  have  made  as 
full  allowance  for  error  as  I  believe  has  been  made,  the 
error  in  this  estimate  does  not  exceed  two  or  three  days. 
For  1909  the  velocity  of  circulation  is  estimated  as  the 
total  circulation  (35.1  billions)  divided  by  the  money  in 
circulation  (1.63  billions),  which  is  21. 5+ ;  that  is,  about 
22  times  a  year,  or  once  in  17  days.  We  conclude  that 
the  velocity  of  circulation  of  money  in  1896  and  the 
velocity  in  1909  were  about  19  and  22  times  respec- 
tively, with  a  probable  error  judged  to  be  about  2  in 
1896  and  not  much  more  than  1  in  1909. 

These  results  would  assign  money  a  slower  circulation 
than  most  of  the  estimates  or  guesses  which  have  been 
made.  We  must  remember,  however,  that  such  persons 
as  economists,  who  are  most  apt  to  think  about  the  circu- 
lation of  money,  have  a  rapid  turnover.  They  are  usu- 
ally city  dwellers  and  the  comparatively  well  to  do,  who, 
as  we  know,  do  not  keep  their  cash  inactive  long. 
Laborers,  especially  thrifty  laborers  and  laborers  paid 
monthly,  will  keep  cash  on  hand  for  several  weeks  with- 
out spending  it.  Farmers  and  others  living  in  sparsely 
settled  districts  will  even  keep  it  for  months.  Probably 
the  velocity  of  circulation  of  money  differs  widely 
among  different  classes  and  different  localities. 

We  may  now  compare  the  years  1896  and  1909  in 
respect  to  money  in  circulation,  deposit  currency,  their 
velocities,  and  their  total  circulation  as  follows:  — 


290         THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

M 

M' 

V 

V 

MV 

M'V 

MV+M'V 

1896 

.87 

2.68 

19 

36 

16 

97 

113 

1909 

1.63 

6.75 

22 

54 

35 

364 

399 

Our  next  task  is  to  interpolate  estimates  for  V  between 
19  in  1896  and  22  in  1909.  The  results  are  given  in  the 
following  table :  — 


Estimates  of   F,  1896  to  1909  * 


1896 
1897 
1898 
1899 
1900 
1901 
1902 


19 

1903 

19 

1904 

20 

1905 

22 

1906 

20 

1907 

22 

1908 

22 

1909 

21 

21 

22 
22 
21 
20 
22 


§  5 

We  have  now  finished  our  statistical  review  of  the 
magnitudes  M,  M',  V,  V,  on  the  left  side  of  the  equation 
of  exchange,  and  have  remaining  only  the  two  magni- 
tudes P,  T,  on  the  right  side  of  the  equation. 

First  we  shall  consider  T.  The  results  of  our  calcula- 
tions are  given  in  the  following  table,  which  expresses 
the  volume  of  trade  in  billions  of  dollars  as  reckoned  at 
the  prices  of  1909:  — 

Estimated  Volume  of  Trade  (in  Billions  op  Dollars  at  Prices 

OF  1909) 


1896 
1897 
1898 
1899 
1900 
1901 
1902 


209 

1903 

239 

1904 

260 

1905 

273 

1906 

275 

1907 

311 

1908 

304 

1909 

335 
324 
378 
396 
412 
381 
399 


^  For  the  method  of  calculating  this  table  see  §  8  of  Appendix 
to  (this)  Chapter  XII. 


Sec.  5]  STATISTICS   OF  RECENT  YEARS  291 

The  table  is  constructed  by  averaging  the  index  num- 
bers of  the  quantities  (not  the  values)  of  trade  in  various 
lines.  The  figures  representing  trade  are  based  on  data 
for  44  articles  of  internal  commerce,  23  articles  of  im- 
port and  25  of  export,  sales  of  stocks,  railroad  freight 
carried,  and  letters  through  the  post  office.  The  final 
figures  are  so  adjusted  that  the  figure  for  1909  shall  be 
399 ;  namely,  the  actual  money  value  of  transactions  in 
that  year  as  worked  out  on  the  other  side  of  the  equa- 
tion {i.e.MV  +M'V').  Relatively  to  each  other,  the 
numbers  for  T  are  independent  of  the  other  side  of  the 
equation.^ 

P.  The  only  remaining  factor  in  the  equation  of  ex- 
change is  the  index  number  of  prices,  P.  Theoretically 
this  could  be  calculated  from  the  other  five  magnitudes 
already  evaluated,  provided  all  our  previous  calculations 
could  be  depended  upon  for  absolute  accuracy.  But 
there  are  possible  errors  in  all  the  magnitudes  M,  M', 
V,  V,  T,  and  such  errors,  should  they  exist,  would  be 
registered  cumulatively  in  P.  It  is  important,  therefore, 
to  check  such  an  indirectly  calculated  value  of  P  by 
directly  calculated  statistics.  By  so  doing  we  are  able 
to  compare  the  P  directly  calculated  and  the  P  in- 
directly calculated.  In  like  manner,  we  might,  if  desired, 
compare  the  directly  and  indirectly  calculated  values 
of  M,  M',  Vj  V,  and  T.  We  shall  confine  ourselves  to 
comparing  the  two  values  of  P,  since  it  is  P  which,  as 
we  have  seen,  is  really  dependent  on  the  five  other  fac- 
tors in  the  equation  of  exchange.  The  values  of  P  (in- 
cluding prices  of  commodities,  securities,  and  labor), 
directly  calculated  in  terms  of  the  figures  for  1909,  as 
100  per  cent,  are  as  follows:  — 

'  For  the  exact  method  (necessarily  laborious)  of  constructing  this 
table  see  §  9  of  the  Appendix  to  (this)  Chapter  XII, 


292        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 
Index  Numbers  of  General  Prices 


1896 
1897 
1898 
1899 
1900 
1901 
1902 


63 

1903 

64 

1904 

66 

1905 

74 

1906 

80 

1907 

84 

1908 

89 

1909 

87 
85 
91 
96 
97 
92 
100 


This  table  is  based  on  the  figures  of  the  Bureau  of 
Labor  for  wholesale  prices.  It  differs  slightly  from  the 
Bureau  of  Labor  figures  owing  to  the  fact  that  we  here 
include  prices  of  securities  and  wages. ^ 

It  remains  to  compare  these  actual  statistics  for  P 
with  P  as  computed  indirectly  from  the  other  magni- 
tudes in  the  equation  of  exchange.  This  calculation 
and  comparison  will  be  given  in  the  following  section. 

§6 

We  have  now  calculated  independently  the  six  magni- 
tudes of  the  equation  of  exchange  for  the  fourteen  years 
1896-1909.  But,  as  already  stated,  we  know  that  these 
six  magnitudes  are  mutually  related  through  the  equa- 
tion of  exchange.  The  question  arises  whether  the 
magnitudeB  as  calculated  will  actually  fulfill  approxi- 
mately the  equation  of  exchange. 

One  way  of  testing  this  question  is  that  adopted  by 
Professor  Kemmerer ;  namely,  to  compare  the  statis- 
tics for  any  one  factor  (say  P),  as  above  directly  calcu- 
lated, with  what  it  would  be  as  indirectly  calculated 
from  the  five  other  magnitudes  in  the  equation  of  ex- 
change. The  following  table  shows  the  value  of  P  as 
obtained  in  these  two  ways  :  — 

*  For  the  method  of  constructing  this  table  se«  §  10  of  Appendix 
to  Cthis)  Chapter  XII. 


Sec.  6] 


STATISTICS   OF   RECENT   YEARS 


293 


Index  Numbers  of  Prices  as  Calculated 


DiREcrrLT 
(P) 

Indirectlt 
/MV  +  M'V'\ 

1896 

63 
64 
66 
74 
80 
84 
89 
87 
85 
91 
97 
97 
92 
100 

54 

1897 

52 

1898 

56 

1899 

69 

1900 

68 

1901 

76 

1902 

82 

1903 

75 

1904 

81 

1905 

83 

1906 

90 

1907 

86 

1908 

87 

1909 

100 

The  agreement  between  the  two  sets  of  figures  is 
visuaUzed  in  Figure  13. 

The  two  values  as  shown  by  the  upper  and  lower 


1^ 


iSUt  ISM'MW  I^BO  004    iSOS  1903  )904  I9QS  i3Q&  iSST  iaOS  (909" 

Fjq.  13. 


294         THE    PURCHASING   POWER  OP  MONEY        [Chap.  XII 

curves  agree  with  each  other  remarkably  well.^  The 
closeness  of  their  agreement  may  be  expressed  in  several 
ways.  One  way  is  to  count  the  agreements  and  dis- 
agreements in  their  changes  of  direction  or  inflections. 
Out  of  12  inflections  in  each  curve  the  two  agree  six 
times,  disagree  three  times,  and  are  neutral  three  times. 
Another  method  is  that  employed  by  Professor  Pearson. 
This  method  consists  in  calculating  what  Professor 
Pearson  calls  a  "correlation  coefficient."  It  shows  an 
agreement  of  97  per  cent  of  perfection  as  compared 
with  23  per  cent  which  Professor  Persons  of  Dart- 
mouth found  for  Professor  Kemmerer's  figures^  for 
1879-1901.  But,  as  already  stated,  a  coefficient  of  cor- 
relation for  successive  data  is  apt  to  be  misleading.  If, 
in  the  case  of  Professor  Kemmerer's  figures,  the  coeffi- 
cient .23  was  an  understatement  of  the  parallelism 
between  his  curves,  the  coefficient  .97  overstates  the 
parallelism  between  mine.  This  overstatement  is 
always  likely  to  result  when  both  of  the  curves  to  be 
compared  rapidly  ascend  or  descend.^ 

The  proper  method  of  applying  a  coefficient  of  cor- 
relation to  successive  data  appears  to  be  to  calculate 

^  The  intermediate  curve  will  be  explained  later. 

'  "Quantity  Theory  as  tested  by  Kemmerer,"  Quarterly  Journal 
of  Economics,  1907-1908,  p.  287. 

3  E.g.  Persons  finds  a  coefficient  of  .98  for  the  correlation  between 
Kemmerer's  figures  for  bank  reserves  and  money  in  circulation 
inclusive  of  bank  reserves,  although  the  two  magnitudes  do  not  show 
any  very  great  agreement  between  fluctuations  in  successive  years, 
but  only  a  general  agreement  in  the  fact  that  both  ascend  rapidly. 
The  coefficient  for  Professor  Kemmerer's  figures  for  P  will  be  much 
higher,  if  instead  of  taking  the  period  beginning  with  1879,  which 
includes  many  years  in  which  prices  do  not  greatly  change,  we  take 
the  period  beginning  at  the  same  time  as  my  own  figures  begin,  viz. 
1896.  The  correlation  coefficient  for  Kemmerer's  figures  1896-1908 
is  83  per  cent,  which  is  far  higher  than  that  obtained  by  Persons  for 
the  period  beginning  in  1879. 


Sec.  6]  STATISTICS   OF   RECENT  YEARS  295 

the  coefficient,  not  for  the  raw  figures,  but  for  their 
successive  year-to-year  ratios.  In  other  words,  we 
tabulate  and  compare  the  ratios  of  each  year's  P  to  the 

preceding  year's  P  and  of  each  year's — to 

the  preceding  year's — If  the  two  sets  of 

ratios  should  rise  or  fall  together,  the  curves  would  show  a 
close  parallelism  or  agreement  in  their  successive  changes 
of  direction.  As  a  matter  of  fact,  the  results  of  this 
method  show  a  coefficient  of  correlation  of  57  per  cent 
(or  .57  ±  .10,  where  .10  is  the  probable  error).  This 
figure,  57  per  cent,  is  a  moderately  high  coefficient  of 
correlation.^  We  may  conclude,  therefore,  that  the 
"quantity  theory"  is  statistically  verified  to  a  high 
degree  of  correlation.^ 

It  is  to  be  emphasized  that  the  coefficients  of  correla- 
tion as  just  given  compare  the  price  level  with  what  it 
should  be  according  to  the  statistics  of  the  jive  magni- 
tudes on  which,  by  the  so-called  quantity  theory,  it  is 
dependent.  The  correlation  would  be  less  if  instead  of 
these  five  magnitudes  only  one  were  taken.  Thus  the 
coefficient  of  correlation  for  1896-1909  as  between 
money,  M,  and  prices,   P,  by  the  year-to-year-ratio 

1  For  instance,  no  one  would  deny  that  the  length  and  breadth 
of  nuts  are  highly  correlated.  The  coefficient  of  their  correlation  is 
57  per  cent.  The  height  of  a  man  and  the  breadth  of  his  face  are 
correlated  to  the  extent  of  35  per  cent. 

2  Incidentally  we  may  here  compare  the  relative  degree  of  corre- 
lation of  Professor  Kemmerer's  figures  and  of  my  own.  For  this 
purpose  we  take  the  period  1896-1908,  which  is  the  longest  period 
common  to  both  investigations.  For  these  years  the  coefficient  for 
my  figures  is  54  per  cent  (or  .54  ±  .11)  as  against  37  per  cent  (or 
.37  ±  .14)  for  Kemmerer's.  These  are  by  the  method  of  year-to- 
year  ratios.  By  the  method  of  raw  figures  my  correlation  is  95  per 
cent  and  Kemmerer's,  83  per  cent. 


296        THE   PUKCHASING   POWER   OF  MONEY        [Chap.  XII 

method  is  43  per  cent  (or  .43  ±  .13).^  Even  this  is  a 
moderately  high  degree  of  correlation. 

If  the  opponents  of  the  ''quantity  theory"  who  at- 
tempt to  disprove  any  relation  between  money  and 
prices  by  pointing  out  the  lack  of  statistical  correspond- 
ence between  the  two  mean  merely  that  other  factors 
besides  money,  M',V,  V,  T,  change  from  time  to  time 
and  that  therefore  the  level  of  prices  does  not  in  actual 
fact  vary  exactly  with  the  quantity  of  money,  their 
contention  is  sound.  But  the  proposition  involved  is  of 
as  little  scientific  consequence  as  the  proposition  that 
the  pressure  of  the  atmosphere  does  not  vary  from  day 
to  day  in  exact  proportion  to  its  density.  We  know 
that,  temperature  being  constant,  the  pressure  of  a  gas 
varies  directly  as  its  density ;  but  that,  as  a  matter  of 
fact,  temperature  seldom  is  constant.  Any  critic  of 
Boyle's  law  who  should  attempt  to  dispute  its  validity 
on  such  a  ground,  however,  would  merely  betray  his 
ignorance  of  the  real  meaning  of  a  scientific  law ;  and  if 
he  should  seriously  attempt  to  ''disprove  it  statistically" 
by  plotting  daily  curves  of  barometric  pressure  and 
atmospheric  density,  he  would  subject  himself  to  scien- 
tific ridicule. 

If  any  one  has  ever  really  imagined  that  the  price  level 
depends  solely  on  the  quantity  of  money,  he  should 
certainly  be  corrected.  But  the  really  important 
matter  is  that  students  of  economics  should  appreciate 
the  existence  of  a  law  of  direct  proportion  between  quan- 
tity of  money  and  price  level  —  a  law  as  real,-  as  im- 
portant, and  as  fundamental  in  the  economic  theory  of 
money,  as  Boyle's  law  of  direct  proportion  between 
density  and  pressure  is  real,  is  important,  and  is  funda- 

1  By  the  (misleading)  direct  comparison  between  M  and  P  the 
coefficient  of  correlation  for  1896-1909  is  97  per  cent. 


Sec.  61  STATISTICS   OF  RECENT  YEARS  297 

mental  in  the  physical  theory  of  gases.  I  beheve  that 
the  frequent  failure  to  realize  the  existence  of  this  law  is 
due  largely  to  the  lack  of  any  clear  conception  of  the 
magnitudes  involved.  M  and  P  seem  to  be  the  only 
magnitudes  which  some  students  really  understand. 
M',  V,  V,  T  are  seldom  discussed  or  even  mentioned. 
But  not  until  the  subject  is  put  on  a  statistical  basis,  — 
in  figures  which  measure  actual  deposit  currency,  ve- 
locities of  circulation,  and  volume  of  trade,  —  will  these 
magnitudes  be  recognized  as  having  a  real  existence  and 
significance. 

But,  to  a  candid  mind,  the  quantity  theory,  in  the 
sense  in  which  we  have  taken  it,  ought  to  appear  suffi- 
ciently secure  without  such  checking.  Its  best  proof 
must  always  be  a  priori,  not  in  the  sense  which  applies 
to  the  proof  of  abstract  mathematical  propositions,  but 
in  the  sense  which  applies  to  the  proof  of  Boyle's  law. 
Thus,  it  is  known  by  induction  that  the  pressure  of  a 
confined  gas  is  caused  by  the  bombardment  of  its  mole- 
cules on  the  containing  walls.  It  is  likewise  known  by 
induction  that  the  pressure  must  be  proportional  to 
the  frequency  of  impact,  provided  the  velocities  of 
the  molecules  are  constant.  Finally,  it  is  known  that 
frequency  of  impact  must  be  proportional  to  the  num- 
ber of  molecules,  i.e.  the  density  of  the  gas,  and  that 
constancy  of  velocity  implies  constancy  of  tempera- 
ture. Therefore,  it  follows  that,  temperature  being 
constant,  pressure  is  proportional  to  density.  Thus, 
from  knowledge  gained  inductively  of  the  individual 
pressures  of  the  molecules  which  compose  the  gas, 
we  may  reason  out  deductively  the  general  pressure 
of  a  gas. 

Analogously,  from  knowledge  gained  inductively  of 
individual  exchanges  —  molecules  as  it  were  —  which 


298         THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 

compose  society's  exchange,  we  may  reason  out  deduc- 
tively the  general  equation  of  exchange. 

Fortunately,  just  as  Boyle's  law  has  been  established 
both  deductively  and  inductively,  we  may  now  assert 
that  the  equation  of  exchange  has  been  sufficiently 
established  both  deductively  and  inductively. 

As  previously  remarked,  to  establish  the  equation  of 
exchange  is  not  completely  to  establish  the  quantity 
theory  of  money,  for  the  equation  does  not  reveal  which 
factors  are  causes  and  which  effects.  But  this  ques- 
tion has  been  answered  in  Chapter  VIII. 

§  7 

To  those  who  have  faith  in  the  a  priori  proof  of 
the  equation  of  exchange  the  real  significance  of  the 
remarkable  agreement  in  our  statistical  results  should 
be  understood  as  a  confirmation,  not  of  the  equation 
by  the  figures,  but  of  the  figures  by  the  equation. 
There  are  discrepancies  in  our  inductive  verification; 
but  these  are  all  well  within  the  limit  of  errors  of  meas- 
urement. The  discrepancies  prove  that  slight  errors 
exist  among  the  figures;  otherwise,  they  would  conform 
exactly  to  the  relation  prescribed  by  the  equation  of 
exchange. 

Our  next  task  is  to  examine  the  discrepancies  and  lo- 
cate, so  far  as  possible,  the  errors  involved.  The  degree 
of  total  mutual  discrepancy  between  the  independently 
calculated  magnitudes  is  best  expressed  by  the  degree 
of  inequality  between  the  calculated  values  of  MF  + 
M'V  and  PT,  which  should  be  equal.  That  is,  PT 
divided  by  MV  +  M'V  should  always  be  unity.  Ac- 
tual division  gives  the  figures  in  the  column  headed 
"  original"  in  the  following  table.  The  other  column 
will  be  explained  presently. 


Sec.  7] 


STATISTICS   OF   RECENT   YEARS 


299 


Ratio  of  PT  to  MV  +  M'  V  as  Calculated 


Original 

RjCDUCSD 

(1) 

(2) 

(3) 

1896 

1.17 

1.06 

1897 

1.24 

1.13 

1898 

1.18 

1.07 

1899 

1.06 

.95 

1900 

1.17 

1.06 

1901 

1.11 

1.00 

1902 

1.08 

.97 

1903 

1.16 

1.05 

1904 

1.06 

.95 

1905 

1.09 

.98 

1906 

1.08 

.97 

1907 

1.13 

1.02 

1908 

1.05 

.94 

1909 

1.00 

.89 

The  figures  in  column  (2)  show  that  the  calculated 
values  oi  PT  are  always  larger  than  the  calculated 
values  of  MV  +  M'V,  the  excess  varying  from  24 
per  cent  to  0  and  averaging  11  per  cent. 

But  these  discrepancies  between  PT  and  MV  +  M'V 
can  be  substantially  diminished  merely  by  changing  the 
base  for  measuring  prices.  This  base  we  have  thus  far 
taken  as  the  price  level  of  1909.  But  as  the  index  num- 
bers have  only  a  relative  significance,  we  are  free  to 
choose  any  other  set  of  numbers  so  long  as  they  maintain 
the  same  relative  magnitudes.  In  accordance  with  this 
prerogative  we  choose  to  reduce  all  the  numbers  for  P 
by  11  per  cent,  this  being  the  average  of  the  original 
discrepancies.  The  result  will  be  to  decrease  PT  by  11 
per  cent  and  to  change  the  series  of  discrepancies  from 
those  shown  in  column  (2)  to  (approximately)  those 
shown  in  column  (3).  These  numbers  vary  from  13  per 
cent  above  to  11  per  cent  below  unity.     These  errors 


300        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 


are  very  small  —  far  smaller  in  fact  than  might  have 
been  expected  in  view  of  the  incomplete  and  unreliable 
character  of  some  of  our  data. 

The  question  remains,  Where  shall  we  place  the  blame 
for  the  errors  which  the  small  existing  discrepancies 
indicate?     Is  the  fault  with  M,  M' ,  V,  V,  P,  or  T? 


,  46^7  l^^e  1099  J^OO  IgOi     1902   1903  1904  4eg»  1906  i.9Q?  190&  (^9 

FiQ.   14. 

How  shall  we  correct  our  calculated  jfigures  ?  We  may 
conclude  on  general  principles  that  the  smallest  correc- 
tions are  the  most  likely  to  be  right.  The  smallest  cor- 
rections imply  a  mutual  adjustment  between  the  six 
factors,  each  adjustment  being  in  the  direction  which 
will  diminish  the  existing  discrepancy.  In  this  way 
each  factor,  as  calculated,  is  regarded  as  having  some 
value,  and  is  given  some  influence  in  correcting  the 


Sec.  7] 


STATISTICS   OP   RECENT   YEARS 


301 


others ;  so  that  any  one  factor  requires  extremely  Uttle 
change.  The  changes  made  in  the  various  factors  are 
made  in  proportion  to  their  assumed  relative  liability  to 
error. 

The  results  are  shown  in  Figures  14,  15,  16,  and  the 
previous  Figure  13,  each  of  which  relates  to  one  of  the 
factors  in  the  equation  of  exchange  as  originally  calcu- 
lated and  as  finally  adjusted  (dotted  lines).   When  they 


'  ■ rr '  •]- 

,,-.«:;,, ::=^I.^ ^--->? 

. _              _             _L. 

: |~"P  'tT^  n^t^t'  itl — 1  i4^f  "1'f 

3E1  cp :» 1  ■"" : d ; ; 

ol1                       ,          1         1 

1897  t%S»   IS99  ISCxi   I3CU    1902   1903  1904-  1903  1806  I907  IS08  1909 

Fig.  15. 


are  all  thus  adjusted,  they  conform  exactly  to  the  equa- 
tion of  exchange.^ 

In  Figure  14  we  see  that  the  alterations  made  in  the 
figures  for  M  and  M'  are  so  trifling  as  to  be  almost  negli- 
gible, being  usually  much  less  than  1  per  cent.  The  al- 
terations in  V  and  V,  which  are  shown  in  Figure  15, 
though  somewhat  greater,  are  also  small,  being  usually 

1  For  the  method  of  adjustment,  see  §  11  of  Appendix  to  (this) 
Chapter  XII. 


302         THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 

less  than  2  per  cent.  The  alterations  in  T,  as  shown  in 
Figure  16,  though  still  greater  than  the  preceding,  are 
nevertheless  so  small  and  uniform  as  to  preserve  an 
almost  perfect  parallelism  between  the  original  and  the 
altered  curve.  The  differences  rarely  exceed  10  per  cent. 
The  alterations  in  P  are  shown  in  the  previous  Figure 
13,  the  upper  curve  representing  the  original  and  the 


--- 



::. 

:;: 

:;":""  :,";::::"  :.":::  ~ ::::::";:"":::;:;:  ^ :: :  "::::;: 

--- 



^ 

900 

::: 

"  ^  —  ;  '  "".;:;.  .".    ..;._      ._;' ::.:..:::;: 

1 

.   , 

__„_    ^           ^     .        _..- 

— 

:: ; 



:~";     _     "_'.';::;. ^.. :.  _            

^ :: 

;;: 

;: 

::::::::: :::-;:i::;;.,-::;;i;;::: :::::::::::::::::::: 

„                        ^-,-         --        -  -         -  -  -  : .- --                                  ---- 

"  - 

:::::::: 

•-%-4i'/'-' --'---+'- --"----' ::::::----:.:: 

"^ 

:::;;:;: 

;:.,.-;:;i::::::::;:::::::;::::-.::::::::::;:::::::::: 

::::■;::] 

... 

h.-' 



--^.|- 

'~.,^  ~ 

+"  "Si 

^ ±__. 

T 

r"" 

H* 

;; 

_-;;_::.;.  .:::::_::  ""::::;:::     ::"   ::   :     ":_;::";: 

--• 

:::]  'la  \ 

M 

5  :ti[i:::]i:-:5n:i^K::-::::::::::::: ;::::::::::::;: 

"  ~  3 

■::::ni 

1  ■ 

TT  iTm  '    n  't'lr 'mT     t               1      '    1                 itl 

iks 

«  i0vy  1 

ito 

ma 

i«o 

ft  iMt    1 

to 

Z   leOS  I9<H   leoS  1906   )907  Id08   I909 

Fig.  16. 


dotted,  or  middle,  curve  representing  the  altered  fig- 
ures for  P.  Here  also  an  extremely  close  parallelism 
between  the  original  and  the  altered  curves  is  evident. 
The  differences  rarely  exceed  3  per  cent. 

Certainly  the  most  exacting  of  critics  could  not  ask 
for  any  greater  consistency  of  results  and  conformity 
to  the  theory  of  the  equation  of  exchange  than  these 
statistics  show.  The  corrections  which  have  been  found 
necessary  to  bring  the  six  figures  as  first  calculated  into 
perfect  agreement  are  smaller  than  the  probable  error 


Bec.  7]  STATISTICS   OF   RECENT   YEARS  303 

in  those  figures  themselves.  I  had  —  quite  antecedently 
to  any  knowledge  of  how  closely  the  final  results  would 
harmonize  —  assigned  certain  rough  estimates  of  the 
probable  errors.  These  are  noted  in  the  Appendix.  The 
probable  error  of  M  is  adjudged  to  be  2  or  3  per  cent ;  of 
M',  2  or  3  per  cent ;  of  F,  5  to  10  per  cent ;  of  V,  5  to 
10  per  cent ;  of  P,  5  to  10  per  cent ;  and  of  T,  5  to  10  per 
cent.  In  other  words,  our  statistical  data  were  regarded 
as  only  rough  or  approximate  ;  yet  the  final  "doctor- 
ing" needed  to  make  them  agree  with  each  other  was,  as 
has  been  seen,  seldom  over  2  per  cent,  being  less  than  1  per 
cent  for  M  and  M' ;  less  than  2  per  cent  for  V  and  V ;  less 
than  3  per  cent  for  P;  and  less  than  4  per  cent  for  T.  We 
conclude  then  that  the  figures  fit  each  other  better  than 
might  be  expected  from  their  known  lack  of  precision. 

The  corrections  which  we  have  assigned  to  the  va- 
rious factors  are  so  insignificant  that  it  would  be  haz- 
ardous to  attempt  to  explain  them  specifically.  The 
errors  which  they  presumably  represent  might  be  due 
to  numerous  sources,  such  as  the  varying  ingredient  in 
the  New  York  clearing  house  transactions  of  bank  trans- 
fers as  distinct  from  ordinary  check  transactions;  or 
such  as  errors  or  defects  in  the  statistics  of  trade  in  grain, 
etc. ;  or  such  as  an  over  or  underestimate  of  the  devia- 
tion from  normal  of  the  particular  days  in  1896  and  1909 
on  which  the  statistics  of  deposits  made  in  banks  were 
gathered;  or  such  as  over  or  underestimates  of  the  un- 
reported deposits,  or  over  or  underestimates  of  the  gold 
in  the  United  States,  or  over  or  underestimates  of  wages 
and  of  other  numerous  minor  though  often  conjectural 
elements  in  our  calculations. 

The  sources  of  error  just  mentioned  were  named 
in  the  order  of  their  probable  importance.  It  is,  per- 
haps, significant  that  the  greatest  discrepancies  are  in 


304        THE    PURCHASING   POWER  OF  MONEY        [Chap.  XII 

the  years  1896-1898,  whose  data  for  T  were  most  defect- 
ive, and  in  1900,  1903,  and  1907,  which  were  years  of 
crises  or  of  impending  crises. 

§8 

After  making  the  above  named  mutual  adjustments 
among  the  six  magnitudes  in  the  equation  of  exchange, 
we  reach  the  following  figures,  constituting  our  final 
table  of  values  for  M,  M',  V,  V\  P,  and  T;  they  are  the 
figures  plotted  in  the  dotted  curves  above  given :  — 

Finally  Adjusted  Values  of  Elements  of  Equation  of 
Exchange  (as  to  1910-1912,  see  p.  492) 


MV  +  M'V 

M 

M' 

V 

v 

P 

T 

MV 

M'V 

PT 

1896  . 

.88 

2.71 

18.8 

36.6 

60.3 

191 

16 

99 

115 

1897  . 

.90 

2.86 

19.9 

39.4 

60.4 

215 

18 

112 

130 

1898  . 

.97 

3.22 

20.2 

40.6 

63.2 

237 

20- 

131- 

150 

1899  . 

1.03 

3.88 

21.5 

42.0 

71.6 

259 

22 

163 

185 

1900  . 

1.18 

4.44 

20.4 

38.3 

76.5 

253 

24 

170 

194 

1901  . 

1.22 

5.13 

21.8 

40.6 

80.5 

291 

27 

208 

235 

1902  . 

1.25 

5.40 

21.6 

40.5 

85.7 

287 

27 

219 

246 

1903  . 

1.39 

5.73 

20.9 

39.7 

82.6 

310 

29 

227 

256 

1904  . 

1.36 

5.77 

20.4 

39.6 

82.6 

310 

28 

228 

256 

1905  . 

1.45 

6.54 

21.6 

42.7 

87.7 

355 

31  + 

279+ 

311 

1906  . 

1.58 

6.81 

21.5 

46.3 

93.2 

375 

34 

315 

349 

1907  . 

1.63 

7.13 

21.3 

45.3 

93.2 

384 

35 

323 

358 

1908  . 

1.62 

6.57 

19.7 

44.8 

90.3 

361 

32 

294 

326 

1909  . 

1.61 

6.68 

21.1 

52.8 

100.0 

387 

34 

353 

387 

1910  . 

1.69 

7.23 

21. 

52.7 

104.0 

399 

34 

381 

415 

1911  . 

1.64 

7.78 

21. 

49.9 

102.2 

413 

34 

388 

422 

1912  . 

1.71 

8.17 

22. 

53.4 

105.3 

450 

38 

436 

474 

This  table,  combining  as  it  does  the  virtues  of  all  the 
independent  calculations  of  M,  M',  V,  V,  P,  T,  with 
the  corrections  of  each  necessary  to  make  it  conform  to 
the  others,  may  be  considered  to  give  the  best  available 
data  concerning  these  magnitudes. 

These  figures,  or  the  dotted  curves  in  the  preceding 
diagram,  show  that  money  in  circulation  (M)  has  nearly 


Sec.  8]  STATISTICS  OF  RECENT  YEARS  305 

doubled  in  thirteen  years ;  that  its  velocity  of  circular 
tion  (F)  has  increased  only  10  per  cent;  that  the  de- 
posit currency  has  nearly  tripled  and  its  velocity  of 
circulation  (V)  has  increased  50  per  cent;  that  the 
volume  of  trade  has  doubled;  and  that  prices  have  risen 
two  thirds. 

These  results  are  not  surprising,  but  are,  I  believe,  just 
such  as  we  might  expect.  Nevertheless,  almost  all  are 
new.  The  figures  for  money  in  circulation  (M)  are  not 
greatly  different  from  those  given  in  official  documents 
and  used  by  Professor  Kemmerer.  Likewise  the  figures 
for  index  numbers  of  prices  are  based  chiefly  on,  and  are 
very  similar  to,  the  index  numbers  for  wholesale  prices 
of  the  United  States  Labor  Bureau.  The  statistics  for 
volume  of  trade  are  constructed  entirely  anew  and  differ 
somewhat  from  Kemmerer's,  which  were  their  only  pre- 
cursors. The  statistics  for  deposits  subject  to  check 
(M')  are  here  published  for  the  first  time.  The  statis- 
tics of  velocities  of  circulation  of  bank  deposits  (V)  are 
the  first  statistics  of  their  kind,  excepting  the  statistics 
for  the  activity  of  bank  accounts  of  European  banks. 
Finally  the  statistics  of  velocity  of  circulation  of  money 
(F)  are  the  first  of  their  kind. 

With  these  data  we  are  able  to  form  a  fairly  correct 
statistical  picture  of  the  circulatory  system  in  the  United 
States.  According  to  the  records  of  1909,  the  money  in 
actual  circulation  (M)  is  1.6  billions  of  dollars  or  $18  per 
capita  (much  less  than  the  official  figure  given  for  circu- 
lation, $35) ;  its  velocity  of  circulation  (F)  is  twenty-one 
times  a  year ;  the  deposit  currency  (ilf' )  is  6.7  billions  or 
$74  per  capita  —  fourfold  that  of  money ;  its  velocity  of 
circulation  (F'),  53  times  a  year  —  two  and  a  half 
times  that  of  money ;  the  total  circulation  of,  or  pay- 
ments by,  money  (MV),  34  billions  a  year ;  the  circula- 


306        THE    PURCHASING   POWER  OF  MONEY        [Chap.  XII 

tion  of  deposits  subject  to  check  or  payments  by  check 
(M'V),  353  bilHons  —  ten  times  as  much  or  nearly  a 
bilUon  a  day.  This  makes  a  grand  total  for  business 
done  at  present  prices  (MV  +  M'V  or  PT)  of  387  bil- 
lions, or  more  than  a  billion  a  day.  The  size  of  this 
aggregate  will  probably  astonish  most  readers.  In  the 
absence  of  actual  statistics  we  have  heretofore  little  real- 
ized the  colossal  proportions  of  our  trade.  Probably  few 
persons  outside  of  statisticians  would  have  imagined 
that  our  import  and  export  trade,  which  has  filled  so 
large  a  place  in  our  political  vision,  sinks  into  utter  insig- 
nificance as  compared  with  the  internal  trade  of  the 
country.  The  total  exports  and  imports  amount  only 
to  a  paltry  3  billions  as  compared  with  a  total  national 
trade  of  387  billions. 

We  are  now  ready  to  represent  the  entire  set  of  figures 
given  in  the  last  table  by  means  of  the  mechanical  illus- 
tration adopted  in  previous  chapters.  This  is  done  in 
Figure  17,  which  shows  at  a  glance  the  course  of  all  the 
six  magnitudes  for  fourteen  years,  making  84  statistical 
figures  in  all.  This  mechanical  picture  visualizes  the 
increase  in  prices  (lengthening  in  right  arm)  which  has 
been  going  on  during  these  fourteen  years,  and  at  the 
same  time  exhibits  the  changes  in  all  the  five  factors  on 
which  that  increase  of  prices  depends.  All  of  the  six 
magnitudes  represented  are,  of  course,  the  corrected  ones, 
so  as  to  exactly  harmonize  with  each  other  and  make 
the  two  sides  of  the  scales  balance.  The  steady 
growth  of  the  money  in  circulation  is  shown  in  the  in- 
crease in  the  size  of  the  hanging  purse ;  the  similar  but 
more  rapid  growth  of  deposits  subject  to  check  is  shown 
by  the  increase  in  the  size  of  the  bank  book ;  the  lesser 
growth  in  the  velocities  of  these  two  media  of  exchange  is 
shown  by  the  lengthening  of  the  two  arms  at  the  left 


■^. 


(usually  from       |^I^,U      three  to  eight  billions). 

The  leverage  of  this  bank  book  represents  V,   the  velocity  of  circulaliao  ("activity^  of  these  deposits      The  < 


The  leverage  of  this  Iray  represents  P,  the  inc 


s  T,  ^e  voluma  of  t 
(or  $1   in  1909, 


r 


^T 


Eia""g w'-nrisz 


frf)"""7a' a'o }!ir 


jEIZmsissse!: 


-^i bi'-'/iT 


-*^ a^""a'o yo""Bb"'"Bi»"' 'itjn ;;b ;^ 


jo' ^'i I'o 'ii;' 0'T"i";k""s""x""'s«""x z a'fe"';x"" 


■x-^-m, .a '  a}'",i'o'' a^ t '  im 


"T SB 'SS X jK-aj^'-'^  '  ;,J'  o'o  ■  Jo '  b^n 


^ 


J& g sa'-iK s-.«;""sti- 


:1L 


""li a, ^t.""ix^' 


'j'      °''"> 


^M     lb' i^i^""'^'-'^' '--j^i^-'-j^^^''' 


;^. .^.i' fc"'''-X' 


:.h k •jr'ns8'''X' 


Jb iW  '"W ,j,-.-g-i"»g'Ti;;(;iii™|; '^gjT'^ X 


w 


Sec.  9]  STATISTICS   OF  RECENT  YEARS  307 

of  the  fulcrum.  These  four  factors  have  all  conspired 
to  increase  prices.  The  only  cause  resisting  the  rise  is 
the  growth  of  trade,  which  is  shown  by  the  increasing 
size  of  the  hanging  tray  at  the  right  and  which  has 
tended  to  reduce  prices. 

We  have  here  a  complete  quantitative  picture  of  the 
causes  affecting  the  price  level  during  the  last  fourteen 
years,  or,  at  any  rate,  of  all  the  'proximate  causes; 
for,  as  we  have  noted,  back  of  the  five  proximate  causes 
lie  innumerable  antecedent  causes. 

What  then,  in  brief,  are  the  facts  of  history  ?  They 
are  that  prices  have  increased  by  about  two  thirds  be- 
tween 1896  and  1909,  that  this  has  been  in  spite  of  a 
doubling  in  the  volume  of  trade,  and  because  of  (1)  a 
doubling  of  money,  (2)  a  tripling  of  deposits,  and  (3 
and  4)  slight  increases  in  the  velocities  of  circulation. 

§9 

There  has  been  much  discussion  as  to  the  most  im- 
portant causes  which  have  increased  prices  during  re- 
cent years.  It  is,  therefore,  interesting  to  compare  the 
four  proximate  causes  which,  as  we  have  seen,  have  alone 
tended  to  increase  prices  in  the  period  1896-1909.  Per- 
haps the  simplest  and  best  method  is  to  compare  the 
actual  rise  of  prices  with  what  it  would  have  been  if 
any  one  cause  of  that  rise  had  been  absent.  That  is, 
we  test  the  importance  of  any  price-raising  factor  by 
answering  the  question.  What  difference  does  it  make 
to  prices  whether  that  factor  is  present  or  absent? 
We  shall  find  that  the  growth  of  money  is  by  far  the  most 
important  cause.  The  growth  of  deposits  is  less  impor- 
tant than  appears  at  first  glance.  The  growth  of  deposits 
would  have  to  be  regarded  as  the  most  important  cause 
if  deposits  could  be  considered  as  independent  of  money. 


308        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 

But  they  are  not  independent.  We  have  seen  that, 
normally,  deposits  rise  or  fall  with  money  in  circulation. 
Therefore,  if  deposits  had  increased  just  as  fast  as  money 
and  no  faster,  we  should  ascribe  the  whole  increase  to 
money  alone.  In  that  case  no  part  of  the  rise  of  prices 
would  be  ascribable  to  any  increase  in  deposits;  for 
there  would  have  been  no  increase  except  what  was  due 
to  the  increase  in  money.  The  increase  of  deposits 
subject  to  check  can  be  considered  independently  of  the 
increase  of  money  only  in  so  far  as  the  deposits  have 
increased  relatively  to  money.  We  have  seen  that  mere 
increase  of  money  would  of  itself  normally  cause  a  pro- 
portionate increase  of  deposits ;  only  the  c^isproportion- 
ate  increase  of  deposits  should  therefore  be  considered 
apart  from  the  increase  in  money  as  a  cause  of  rising 
prices.  Therefore  the  true  method  of  considering  de- 
posits as  a  separate  cause  appears  to  be  to  reckon  them 

M' 

relatively    to  money.      That  is,  not  M',   but  -jtt  is 

the  magnitude  to  be  considered.^ 

We  may  therefore  consider  as  the  only  causes  tending 
to  raise  prices  during  the  period  1896-1909,  the  follow- 
ing four :  — 

(1)  The  increase  in  money  in  circulation,  i.e.  the  in- 
crease in  M. 

(2)  The  increase  in  relative  deposits,  i.e.  the  increase 
.    AI' 

M 

(3)  The  increase  in  the  velocity  of  circulation  of 
money,  i.e.  the  increase  in  V. 

(4)  The  increase  in  the  velocity  of  circulation  of  de- 
posits, i.e.  the  increase  in  V. 

1  See  §  1  of  Appendix  to  Chapter  III,  where  this  magnitude  (rela- 
tive deposits)  is  treated  and  represented  by  the  letter  k. 


Sec.  9]  STATISTICS  OF  KECENT  YEARS  309 

The  fifth  factor  determining  the  price  level,  viz. 
the  factor  T  has,  as  we  have  seen,  tended  to  lower 
prices. 

We  shall  now  proceed  to  note  what  would  be  the  sepa- 
rate effects  on  prices  of  these  four  price-raising  causes 
and  of  the  one  price-depressing  cause. 

We  wish,  then,  to  know  what  the  price  level  would 
have  been  in  1909  under  the  following  five  conditions  :  — 

(1)  If  the  money  in  circulation  {M)  had  not  grown 
at  all  since  1896, 

M' 

(2)  If  the  relative  deposits  —  had  not  grown  at  all 

since  1896, 

(3)  If  the  velocity  of  circulation  of  money  (F)  had 
not  grown  at  all  since  1896, 

(4)  If  the  velocity  of  circulation  of  deposits  {V)  had 
not  grown  at  all  since  1896, 

(5)  If  the  volume  of  trade  {T)  had  not  grown  at  all 
since  1896, 

assuming  in  each  case  that  all  the  other  four  factors 
had  grown  in  exactly  the  way  they  did  grow.  We  have 
taken  the  actual  price  level  in  1909  as  100  per  cent  and 
shall  continue  to  do  so,  expressing  on  this  basis  what 
the  price  level  would  have  been  under  each  of  the  five 
hypotheses  above  named.  We  reach  the  following 
results  :  ^  — 

1  The  calculations  needed  are  obvious  and  simple.  They  consist 
of  substituting,  for  all  the  factors  but  one  in  the  right  side  of  the 

equation  P  =  —    "^  = ^^^ '- — .  the  statistics  already 

obtained  for  1909,  and  for  that  one  factor  remaining,  the  figure  for 
1896.  This  one  factor  remaining  is,  for  the  first  hjrpothesis,  M ; 
for  the  second,  M' /  M ;  for  the  third,  V ;  the  fourth,  V  \  and  the 
fifth  T. 


310        THE   PURCHASING   POWER   OF  MONEY        (Chap.  XH 

Were  it  not  for  the  growth  of 

(1)  Money  (M),  the  price  level  of  1909  would  have 
been  55  instead  of  100; 

(2)  Relative  deposits  [jir],  the  price   level  of  1909 

would  have  been  77  instead  of  100; 

(3)  Velocity  of  circulation  of  money  (F),  the  price 
level  of  1909  would  have  been  99  instead  of  100; 

(4)  Velocity  of  circulation  of  deposits  (F'),  the  price 
level  of  1909  would  have  been  72  instead  of  100; 

(5)  Volume  of  trade  (T),  the  price  level  of  1909  would 
have  been  206  instead  of  100. 

In  other  words,  were  it  not  for  the  growth  of 

(1)  Money  (M),  prices  would  have  been  45  per  cent 
lower; 

(2)  Relative  deposits  (77- J,  prices  would  have  been 

23  per  cent  lower; 

(3)  Velocity  of  money  (V),  prices  would  have  been  1 
per  cent  lower; 

(4)  Velocity  of  deposits  (V),  prices  would  have  been 
28  per  cent  lower. 

(5)  Volume  of  trade  (7^,  prices  would  have  been  106 
per  cent  higher. 

The  four  price-raising  causes  may,  therefore,  be 
arranged  in  the  following  order  of  relative  impor- 
tance :  — 

Except  for  the  growth  of  V,  prices  would  have  been 

1  per  cent  lower  than  they  were. 

M' 
Except  for  the  growth  of  — -,  prices  would  have  been 

23  per  cent  lower  than  they  were. 

Except  for  the  growth  of  F',  prices  would  have  been 
28  per  cent  lower  than  they  were. 


Sec.  10]  STATISTICS  OP  RECENT  YEARS  311 

Except  for  the  growth  of  M,  prices  would  have  been 
45  per  cent  lower  than  they  were. 

We  conclude,  therefore,  that  the  growth  of  the  velocity 
of  circulation  of  money  was  a  negligible  factor  in  raising 
prices ;  that  the  relative  growth  of  deposits  and  their 
velocity  were  large  factors ;  and  that  the  growth  of 
money  was  the  largest.  The  importance  of  the  growth 
of  money  as  a  price-raising  factor  was,  according  to  the 
above  figures,  almost  exactly  double  that  of  relative 
deposits  and  a  little  over  50  per  cent  greater  than  that 
of  their  velocity  of  circulation. 

§10 

But  the  full  effect  of  the  increase  in  the  quantity  of 
money  is  really  greater  even  than  these  figures  indicate  ; 
for  we  have  not  included  the  effect  of  the  overflow  of 
money  abroad,  caused  by  the  great  increase  in  Ameri- 
can bank  deposits.  Evidently  this  overflow  must  be 
taken  into  account;  for  the  other  three  price-raising 
factors,  by  crowding  out  money  and  usurping  its  place, 
have  given  themselves  an  exaggerated  appearance  of 
importance.  In  other  words,  there  has  been  a  greater 
increase  in  money  than  appears  from  the  United  States 
figures  by  the  amount  which  has  overflowed  into  foreign 
lands.  The  United  States  is  only  a  small  part  of  the 
world's  market,  and  its  price  level  is  largely  determined 
by  the  world's  price  level.  Whatever  raises  prices  in 
one  country  tends  to  raise  prices  in  all  countries,  and  in 
the  last  analysis  the  only  correct  way  to  measure  the 
relative  importance  of  price-raising  causes  is  to  consider 
the  world  as  a  whole.  If  the  statistics  we  have  worked 
out  for  the  United  States  were  typical  of  the  world, 
the  resulting  estimate  of  the  relative  importance  of  the 
four  price-raising  causes  would  be  true  of  the  world. 


312        THE    PURCHASING   POWER   OF  MONEY        [Chap.  XII 

But  there  is  strong  reason  to  believe  that  the  growth  of 
deposits  and  of  their  velocity  played  a  far  greater 
part  in  raising  prices  in  the  United  States  than  anywhere 
else.  The  reason  is  that  banking  is  in  its  infancy  in 
France  and  most  other  countries.  It  is  so  unimportant 
that  even  if  its  rate  of  growth  there  were  prodigious,  it 
would  still  be  a  relatively  insignificant  price-raising 
factor.  We  may  therefore  be  certain,  humanly  speak- 
ing, that  outside  of  the  United  States  the  increase  of 
prices  is  even  more  largely  due  to  the  growth  of  money 
(gold)  than  in  the  United  States. 

We  conclude,  therefore,  with  much  confidence,  that 
the  increase  in  the  world's  gold  is  chiefly  responsible  for 
the  increase  in  the  world's  prices.  What  has  been  said 
probably  explains  why,  in  the  last  three  years,  there  has 
been  no  actual  increase  in  the  quantity  of  money  in  cir- 
culation in  the  United  States.  It  has  been  crowded  out 
or  prevented  from  increasing  by  the  excessively  great 
increase  of  our  deposits  and  of  their  velocity  of  circula- 
tion. 

But  besides  the  world  movements  of  prices  there  are 
special  local  movements  as  well.  Anything  which  in- 
terferes with  trade,  like  a  tariff,  tends  to  make  the  rise 
of  prices  unequal.  There  remains,  therefore,  the  ques- 
tion of  such  special  influences  on  the  American  price 
level  as  the  tariff,  —  working  out  its  effects  through  M. 

As  we  have  seen  in  a  previous  chapter,  the  effect  of  en- 
acting a  protective  tariff  is  to  raise  the  price  level  of 
the  "protected"  country  by  creating  temporarily  a 
''favorable"  balance  of  trade  and  thus  stimulating  im- 
ports of  the  money  metal  and  discouraging  its  export. 
This  effect  ceases  as  soon  as  the  price  level  at  home  has 
been  elevated  enough,  relatively  to  the  price  levels  abroad, 
to  restore  the  equilibrium  of  trade  and  stop  the  relative 


Sec.  10]  STATISTICS   OF  RECENT  YEARS  313 

accumulation  of  gold  in  the  protected  country.  There- 
after the  tariff  ceases  to  affect  the  price  level, 
except  as  it  interferes  with  trade  and  thereby  prevents 
the  price  level  at  home  from  adjusting  itself  to  the  price 
levels  abroad.  This  interfering  effect  may  be  in  either 
direction;  that  is,  the  price  level  at  home  will  be  ren- 
dered more  independent  of  foreign  price  levels  than  it 
would  be  if  trade  were  free.  The  tariff  merely  isolates 
the  protected  country. 

During  the  period  under  investigation,  1896-1909, 
there  have  been  two  changes  in  the  tariff,  that  of  1897, 
and  the  more  recent  law  of  1909.  The  first  represented 
an  advance  over  the  rates  of  1894.  This  law  of  1897 
must  have  tended,  therefore,  somewhat  to  restrict  im- 
ports and  to  raise  prices.  So  far  as  our  prices  have 
risen  faster  than  prices  have  risen  in  other  countries, 
like  England,  in  the  period  here  considered,  it  seems 
fair  to  attribute  a  part  of  this  additional  rise  to  our 
tariff  system. 

We  come  finally  to  the  tariff  of  1909.  This  act  is 
so  recent  as  scarcely  yet  to  have  had  much  perceptible 
influence,  even  if  that  influence  be  assumed  to  have 
begun  as  soon  as  the  act  was  planned,  early  in  1909. 
There  has  waged  a  bitter  political  controversy  over  the 
question  whether  it  was  a  revision  upward  or  downward. 
The  best  unbiased  opinion  seems  to  be  that  it  was 
slightly  upward  but  was  chiefly  a  mere  rearrangement 
by  which  some  duties  were  raised  and  others  lowered. 
These  conclusions  of  Professor  Taussig,  Professor  Willis, 
and  others  are  based  on  an  intensive  study  of  the  tariff 
schedules. 

A  review  of  the  statistics  of  the  equation  of  exchange  is 
entirely  consistent  with  these  conclusions.  This  consist- 
ency may  not  be  evident  at  first  glance.    On  the  con- 


314        THE   PURCHASING   POWER  OF  MONEY        [Chap.  XII 

trary,  those  who  claim  that  duties  have  been  greatly 
increased  might  point  to  the  fact  that  since  the  tariff 
American  prices  have  risen  faster  than  English  prices  ;* 
while  those  who  claim  that  the  revision  was  distinctly 
downward  might  point  to  the  increase  in  our  imports  of 
commodities,  and  the  increase  in  our  exports  of  gold. 
But  these  seemingly  discordant  facts  are  reconcilable. 

American  statistics  show  that  there  has  been  an  enor- 
mous expansion  in  bank  deposits  and  in  their  velocity 
of  circulation  in  1909  as  compared  with  1908.  This 
would  naturally  have  the  effect  of  raising  American 
prices,  displacing  gold,  and  checking  the  increase  of 
money  in  circulation  in  the  United  States,  which  would 
otherwise  occur,  and  correspondingly  of  encouraging  the 
import  of  commodities.  The  facts  agree  precisely  with 
these  known  tendencies.  Prices  in  the  United  States  have 
risen  more  than  in  England,  the  increase  in  the  quantity 
of  money  in  circulation  has  been  checked,  the  export  of 
gold  and  the  import  of  commodities  have  been  increased. 
Thus  we  may  explain  all  the  facts  without  assuming 
the  tariff  as  a  disturbing  element.^ 

It  would  take  us  too  far  afield  to  discuss  all  the  other 
factors  which  have  been  held  more  or  less  responsible  for 
the  increase  in  prices.    We  have  already  made  it  clear 


*  Beyond  1909  only  American  figures  are  available.  Those  in 
the  Bulletin  of  the  United  States  Bureau  of  Labor  show  an  uninter- 
rupted rise  in  prices  from  January,  1909,  to  March,  1910.  Between 
these  dates  the  index  numbers  for  wholesale  prices  rose  from  124.0 
to  133.8.  For  a  good  English-American  comparison,  see  Report  of  the 
(Mass.)  Commission  on  the  Cost  of  Living.    Boston,  1910,  pp.  26,  56. 

2  But,  although  we  cannot  justly  convict  the  tariff  of  raising  our 
price  level  in  recent  years,  it  is  of  course  true  that  a  reduction  in  the 
tariff  would  tend  powerfully  to  reduce  that  level ;  for,  as  we  have  seen, 
a  tariff  wall  acts  like  a  dam  in  keeping  up  the  high  level  accumulated 
by  the  original  imposition  of  duties. 


Sec.  11]  STATISTICS  OF  RECENT  YEARS  315 

that  none  of  these  could  influence  prices  except  by  in- 
creasing the  quantity  of  money  in  circulation,  the  rela- 
tive deposits,  or  their  velocities,  or  by  decreasing  trade. 
As  trade  has  increased  greatly,  the  last  possibility  may 
be  ignored. 

As  to  the  causes  which  have  increased  money  and  de- 
posits and  their  velocities,  the  most  important  seem  to 
be  the  following  :  — 

( 1 )  The  chief  cause  of  the  increase  of  money  has  been  the 
increase  in  gold  mining.  Bank  notes  have  only  slightly 
more  than  kept  pace  with  other  money  in  circulation. 

(2)  The  chief  causes  of  the  relative  increase  in 
bank  deposits  seem  to  have  been  those  which 
have  extended  banking  especially  in  the  South. 
The  recent  banking  laws,  encouraging  the  establish- 
ment of  small  banks,  may  have  had  some  part  in  this 
extension. 

(3)  The  chief  cause  of  the  increase  of  velocity  of  cir- 
culation, especially  of  bank  deposits,  seems  to  have  been 
the  concentration  of  population  in  cities.  We  have 
seen  that  the  larger  the  town  the  greater  the  velocity  of 
circulation  of  bank  deposits. 

§  11 
Throughout  this  book  we  have  aimed  at  explaining 
the  general  purchasing  power  of  money,  not  its  purchas- 
ing power  over  any  particular  goods  or  class  of  goods. 
The  problem  of  the  rise  in  "  the  cost  of  living  "  is  partly 
a  general  problem  of  the  purchasing  power  of  money, 
and  partly  a  special  problem  of  the  prices  of  food,  cloth- 
ing and  other  costs  of  "  living."  With  the  special 
problem  we  have  here  nothing  to  do.  But  it  so  hap- 
pens that  the  special  changes  in  the  cost  of  living  are 
very  small  as   compared  with  the  general   change  in 


316         THE   PURCHASING   POWER   OF  MONEY        [Chap.  XII 

prices.  At  any  rate  this  is  true  of  the  wholesale  prices 
of  food.  The  index  number  of  food  rose  between  Jan- 
uary, 1909,  and  March,  1910,  from  122.6  to  130.9,  while 
general  wholesale  prices  rose  from  124.0  to  133.8;  that 
is,  the  special  prices  of  food  rose  about  evenly  with  the 
general  rising  tide  of  prices.  So  far  as  there  was  any 
difference  it  was  such  that  the  special  prices  rose  slightly 
less  than  general  prices.  The  "general  prices"  here 
referred  to  are  only  wholesale  prices  and  do  not  include 
prices  of  labor  and  securities;  but  the  inclusion  of  these 
elements,  judging  from  the  statistics  as  already  given 
up  to  1909,  and  market  reports  since  that  date,  would 
not  materially  change  the  result. 

j  We  conclude  that  the  "rise  in  the  cost  of  living"  is 
no  special  movement  of  food  prices  nor,  presumably,  of 
other  particular  prices,  but  is  merely  a  part  of  the  gen- 
eral movement  of  prices.  The  cost  of  living  is  swept 
along  with  the  general  rising  tide  of  prices  of  all  sorts. 
It  indicates  little  or  no  special  change  in  the  supply 
or  demand  of  special  classes  of  goods,  but  simply 
reflects  the  fall  in  the  general  purchasing  power  of 
money.  These  remarks  apply  not  simply  to  the 
months  beginning  w  th  January,  1909,  but  back  to 
1908.  Back  of  1908  food  prices  move  somewhat  ir- 
regularly as  compared  with  general  prices,  but  on  the 
whole  maintain  an  approximately  even  pace  from  1897 
to  1909. 

The  following  table  gives  some  interesting  by-prod- 
ucts of  our  study  for  the  period  1896-1909. 

We  note  from  column  (2)  that  deposits  {M')  have 
grown,  not  only  absolutely,  but  relatively  to  money 
(M),  changing,  from  a  little  over  threefold  to  a  little 
over  fourfold  the  money  in  circulation.  The  figure  for 
the  panic  year,  1907,  was   the  highest   but  one,  and 


Sec.  Ill 


STATISTICS   OF   RECENT   YEARS 


317 


the  drop  in  the  succeeding  year  was  the  largest  drop 
in  the  table. 

Column  (3)  shows  the  "virtual"  velocity  of  money, 
based  on  the  idea  that  the  total  work  of  exchange,  even 
that  performed  by  checks,  is  really  the  work,  indirectly, 
of  money.  It  is  simply  the  quotient  of  the  total  ex- 
change work  done,  divided  by  the  total  money  in  circula- 
tion and  in  banks. 


(1) 

(2) 

(3) 

(4) 

(5) 

Ml 

M 

Virtual 
Velocity 

MV 

M'V 

MV+M'V 

MV+M'V 

1896 

3.1 

80 

.14 

.86 

1897 

3.2 

84 

.14 

.86 

1898 

3.3 

89 

.13 

.87 

1899 

3.8 

103 

.12 

.88 

1900 

3.6 

99 

.12 

.88 

1901 

4.2 

114 

.11 

.89 

1902 

4.3 

115 

.11 

.89 

1903 

4.1 

113 

.11 

.89 

1904 

4.2 

107 

.11 

.89 

1905 

4.5 

125 

.10 

.90 

1906 

4.3 

132 

.10 

.90 

1907 

4.4 

129 

.10 

.90 

1908 

4.0 

107 

.10 

.90 

1909 

4.1 

124 

.09 

.91 

1910  (see  p.  492)   .     . 

4.4 

134 

.08 

.92 

1911      "    "       "      .     . 

4.7 

131 

.08 

.92 

1912     "    "       "      .     . 

4.8 

144 

.08 

.92 

We  note  that  this  virtual  velocity  of  circulation  of 
monej^,  or  its  efficiency  in  providing  for  exchanges,  has 
grown  about  50  per  cent.  Its  growth  has  been  inter- 
rupted by  occasional  slumps,  but  all  of  these  were  trifling 
excepting  that  following  the  crisis  of  1907. 

The  fourth  and  fifth  columns  give  the  solution  of  the 
much  mooted  question  of  the  relative  importance  of 
check    transactions    {M'V)    and   money    transactions 


318       THE    PURCHASING   POWER  OF  MONEY        [Chap.  XII 

(MV),  —  a  question  to  which  many  writers,  including 
Professor  Kinley,  have  given  much  attention.  We  find 
that  in  1896  about  14  per  cent  of  the  business  in  the 
United  States  was  performed  by  money  and  in  1909 
about  9  per  cent.  In  other  words,  checks  performed  in 
1896  about  86  per  cent  of  the  total  exchange  work,  and 
in  1909  about  91  per  cent.^ 

These  figures  appear  to  afford  the  first  fairly  precise 
determination  of  the  relative  importance  of  check  and 
money  transactions.  They  confirm  the  belief  ^  that  the 
relative  part  played  by  checks  in  the  country's  trans- 
actions has  substantially  increased.  The  prevailing  im- 
pression that  they  constitute  nine  tenths  of  all  transac- 
tions is  also  seen  to  be  correct. 

^  For  discussion  of  these  figures,  see  §  12  of  the  Appendix  to  (this) 
Chapter  XII,  where  comparison  is  made  with  Professor  Kinley 's 
results. 

*  See  e.g.  Cannon  on  Clearing  Houses  among  the  Reports  of  the 
Monetary  Commission,  1910. 


CHAPTER  XIII 

THE   PROBLEM   OF  MAKING   PURCHASING   POWER  MORE 

STABLE 

§1 

We  have  seen  that  the  purchasing  power  of  money 
(or  its  reciprocal,  the  level  of  prices)  depends  exclu- 
sively on  five  factors,  viz. :  the  quantity  of  money  in  cir- 
culation, its  velocity  of  circulation,  the  quantity  of 
deposits  subject  to  check,  its  velocity,  and  the  volume 
of  trade.  Each  of  these  five  magnitudes  depends  on 
numerous  antecedent  causes,  but  they  do  not  depend 
on  each  other  except  that: — 

(1)  Deposits  subject  to  check  depend  on  money  in 
circulation,  the  two  normally  varying  in  unison. 

(2)  The  velocities  of  circulation  of  money  and  deposits 
tend  to  increase  with  an  increase  in  the  volume  of  trade. 

(3)  Any  two  or  more  of  the  five  factors  may  be  in- 
directly related  by  virtue  of  being  dependent  on  a  com- 
mon cause  or  causes.  Thus,  the  same  invention  may 
cause  an  increase  in  both  velocities,  or  in  both  money 
and  trade,  or  in  both  deposits  and  their  velocity.  To 
take  an  historical  case,  we  know  that  the  growing 
density  of  population  has  operated  to  increase  all  of 
the  five  factors. 

(4)  During  transition  periods  certain  temporary  dis- 
turbances or  oscillations  occur  in  all  six  magnitudes,  the 
extremes  of  which  are  crises  and  depressions.  Normally, 
the  price  level  is  an  effect  and  not  a  cause  in  the  equation 

319 


320       THE    PURCHASING   POWER   OF   MONEY       [Chap.  XIII 

of  exchange;  but  during  such  transition  periods  its 
fluctuations  temporarily  react  on  the  other  five  factors, 
and  especially  on  deposits.  A  rise  will  thus  temporarily 
generate  a  further  rise,  while  a  fall  temporarily  operates 
in  the  opposite  direction. 

The  price  level,  then,  is  the  result  of  the  five  great 
causes  mentioned,  normally  varying  directly  with  the 
quantity  of  money  (and  with  deposits  which  normally 
vary  in  unison  with  the  quantity  of  money),  provided 
that  the  velocities  of  circulation  and  the  volume  of 
trade  remain  unchanged,  and  that  there  be  a  given 
state  of  development  of  deposit  banking.  This  is  one 
of  the  chief  propositions  concerning  the  level  of  prices 
or  its  reciprocal,  the  purchasing  power  of  money.  It 
constitutes  the  so-called  quantity  theory  of  money. 
The  qualifying  adverb  "  normally";  is  inserted  in  the 
formulation  in  order  to  provide  for  the  transitional 
periods  or  credit  cycles.  Practically,  this  proposition  is 
an  exact  law  of  proportion,  as  exact  and  as  fundamental 
in  economic  science  as  the  exact  law  of  proportion  be- 
tween pressure  and  density  of  gases  in  physics,  assum- 
ing temperature  to  remain  the  same.  It  is,  of  course? 
true  that,  in  practice,  velocities  and  trade  seldom  re- 
main unchanged,  just  as  it  seldom  happens  that  tem- 
perature remains  unchanged.  But  the  tendency  repre- 
sented in  the  quantity  theory  remains  true,  whatever 
happens  to  the  other  elements  involved,  just  as  the 
tendency  represented  in  the  density  theory  remains  true 
whatever  happens  to  temperature.  Only  those  who  fail 
to  grasp  the  significance  of  what  a  scientific  law  really 
is  can  fail  to  see  the  significance  and  importance  of  the 
quantitative  law  of  money.  A  scientific  law  is  not  a 
formulation  of  statistics  or  of  history.  It  is  a  formula- 
tion of  what  holds  true  under  given  conditions.     Sta- 


Sec.  1]        IS  THE    PRICE   LEVEL   CONTROLLABLE  ?  321 

tistics  and  history  can  be  used  to  illustrate  and  verify 
laws  only  by  making  suitable  allowances  for  changed 
conditions.  It  is  by  making  such  allowances  that  we 
have  pursued  our  study  of  the  last  ten  centuries  in  the 
rough  and  of  the  last  decade  and  a  half  in  detail.  In 
each  case  we  found  the  facts  in  accord  with  the  princi- 
ples previously  formulated. 

From  a  practical  point  of  view  the  most  serious  prob- 
lem revealed  by  this  historical  and  statistical  study  is 
the  problem  of  stability  and  dependability  in  the  pur- 
chasing power  of  money.  We  find  that  this  purchasing 
power  is  subject  to  wide  variations  in  two  ways:  (1)  It 
oscillates  up  and  down  with  the  transitional  periods 
constituting  credit  cycles;  and  (2)  it  is  likely  to  suffer 
secular  variations  in  either  direction  according  to  the 
incidents  of  industrial  changes.  The  first  transition  is 
connected  with  the  banking  system;  the  second  depends 
largely  upon  the  money  metal. 

One  method  of  mitigating  both  of  these  evils  is  the 
increase  of  knowledge  as  to  prospective  price  levels. 
As  we  have  seen,  the  real  evils  of  changing  price  levels 
do  not  lie  in  these  changes  per  se,  but  in  the  fact  that 
they  usually  take  us  unawares.  It  has  been  shown  that 
to  be  forewarned  is  to  be  forearmed,  and  that  a  fore- 
known change  in  price  levels  might  be  so  taken  into 
account  in  the  rate  of  interest  as  to  neutralize  its  evils. 
While  we  cannot  expect  our  knowledge  of  the  future 
ever  to  become  so  perfect  as  to  reach  this  ideal,  viz. 
compensations  for  every  price  fluctuation  by  corre- 
sponding adjustments  in  the  rate  of  interest  —  never- 
theless every  increase  in  our  knowledge  carries  us  a 
little  nearer  that  remote  ideal.  Fortunately,  such  in- 
crease in  knowledge  is  now  going  on  rapidly.  The  edi- 
tors of  trade  journals  to-day  scan  the  economic  horizon 


322       THE    PURCHASING    POWER   OF   MONEY       [Chap.  XIII 

as  weather  predictors  scan  the  physical  horizon;  and 
every  indication  of  a  change  in  the  economic  weather 
is  noted  and  commented  upon.  Within  the  past  year  a 
certain  firm  has  instituted  a  statistical  service  to  supply 
bankers,  brokers,  and  merchants  with  records,  or  "busi- 
ness barometers,"  and  forecasts  based  thereon,  with  the 
avowed  object  of  preventing  panics.  Yet  it  is  probably 
in  regard  to  the  fundamental  mechanism  by  which  such 
forecasts  are  based  that  there  is  the  greatest  need  of  a 
wider  diffusion  of  knowledge.  The  range  of  the  ordi- 
nary business  man's  theoretical  knowledge  is  extremely 
narrow.  He  is  even  apt  to  be  suspicious  of  such 
knowledge,  if  not  to  hold  it  in  contempt.  The  conse- 
quences of  this  narrowness  are  often  disastrous,  as,  for 
instance,  when,  in  pursuance  of  the  advice  of  New  York 
business  men.  Secretary  Chase  issued  the  greenbacks,  or 
when  the  ill-advised  legislation  to  close  the  Gold  Room 
was  enacted.  And  it  is  not  altogether  in  unusual  pre- 
dicaments such  as  those  brought  by  the  Civil  War  that 
the  business  man's  Umitations  in  knowledge  react  in- 
juriously upon  him.  Every  day  he  is  hampered  by  a 
lack  of  understanding  of  the  principles  regulating  the 
purchasing  power  of  money;  and  in  proportion  as  he 
fails  to  understand  these  principles  he  is  apt  to  fail  in 
predictions.  The  prejudice  of  business  men  against 
the  variability  of,  and  especially  against  a  rise  of  the 
rate  of  interest,  probably  stands  in  the  way  of  prompt 
adjustment  in  that  rate  and  helps  to  aggravate  the  far 
more  harmful  variability  in  the  level  of  prices  and  its 
reciprocal,  the  purchasing  power  of  money.  The  busi- 
ness man  has,  in  fact,  never  regarded  it  as  a  part  of 
the  preparation  for  his  work  to  understand  the  broad 
principles  affecting  money  and  interest.  He  has  rather 
assumed  that  his  province  was  confined  to  accumu- 


Sec.  2]         IS  THE    PRICE   LEVEL   CONTROLLABLE  ?  323 

lating  a  technical  acquaintance  with  the  nature  of  the 
goods  he  handles.  The  sugar  merchant  informs  him- 
self as  to  sugar,  the  grain  merchant  as  to  grain,  the 
real  estate  trader  as  to  real  estate.  It  scarcely  occurs 
to  any  of  them  that  he  needs  a  knowledge  as  to  gold; 
yet  every  bargain  into  which  he  enters  depends  for 
one  of  its  two  terms  on  gold.  I  cannot  but  beUeve 
that  the  diffusion  among  business  men  of  the  fuller 
knowledge  of  the  equation  of  exchange,  of  the  relation 
of  money  to  deposits,  of  credit  cycles  and  of  interest, 
which  the  future  is  sure  to  bring,  will  pay  rich  returns 
in  mitigating  the  evils  of  crises  and  depressions  which 
now  take  them  so  often  unawares. 

§2 

But  while  there  is  much  to  be  hoped  for  from  a  greater 
foreknowledge  of  price  changes,  a  lessening  of  the  price 
changes  themselves  would  be  still  more  desirable.  Va- 
rious preventives  of  price  changes  have  been  proposed. 
We  shall  first  consider  those  which  are  more  particularly 
applicable  to  secular  price  changes,  and  afterward  con- 
sider those  more  particularly  applicable  to  the  price 
changes  involved  in  credit  cycles.  The  secular  price 
changes  are,  as  we  have  seen,  chiefly  due  to  changes  in 
money  and  in  trade.  There  has  been  for  centuries,  and 
promises  to  be  for  centuries  to  come,  a  race  between 
money  and  trade.  On  the  results  of  that  race  depends  to 
some  extent  the  fate  of  every  business  man.  The  com- 
mercial world  has  become  more  and  more  committed  to 
the  gold  standard  through  a  series  of  historical  events 
having  little  if  any  connection  with  the  fitness  of  that  or 
any  other  metal  to  serve  as  a  stable  standard.  So  far  as 
the  question  of  monetary  stability  is  concerned,  it  is 
not  too  much  to  say  that  we  have  hit  upon  the  gold 


324       THE    PURCHASING   POWER   OF  MONEY       [Chap.  XIII 

standard  by  accident  just  as  we  hit  on  the  present  rail- 
way gauge  by  the  accident  of  previous  custom  as  to 
road  carriages ;  and  just  as  we  hit  upon  the  decimal 
notation  by  the  accident  of  having  had  ten  fingers,  and 
quite  without  reference  to  the  question  of  numerical 
convenience  in  which  other  systems  of  numeration 
would  be  superior.  Now  that  we  have  adopted  a  gold 
standard,  it  is  almost  as  difficult  to  substitute  another 
as  it  would  be  to  establish  the  Russian  railway  gauge 
or  the  duodecimal  system  of  numeration.  And  the 
fact  that  the  question  of  a  monetary  standard  ■  is  to- 
day so  much  an  international  question  makes  it  all 
the  more  difficult.  Yet,  as  Professor  Shaler,  the  geol- 
ogist, has  said,  ''  It  seems  likely  that  we  shall,  within 
a  few  decades,  contrive  some  other  means  of  measur- 
ing values  than  by  the  ancient  device  of  balancing 
them  against  a  substance  of  which  the  supply  is  ex- 
cessive." ^ 

I  shall  not  attempt  to  offer  any  immediate  solution 
of  this  great  world  problem  of  finding  a  substitute 
for  gold.  Before  a  substitute  for  gold  can  be  found, 
there  must  be  much  investigation  and  education  of 
the  public.  The  object  here  is  to  call  attention  to 
the  necessity  for  this  investigation  and  education, 
to  examine  such  solutions  as  have  been  already  pro- 
posed and,  very  tentatively,  to  make  a  suggestion  which 
may  possibly  be  acted  upon  at  some  future  time, 
when,  through  the  diffusion  of  knowledge,  better  statis- 
tics, and  better  government,  the  time  shall  become 
ripe. 

One  suggestion  has  been  to  readopt  bimetallism.  This 
has  already  been  discussed  in  Chapter  VII.  We  were 
then  concerned,  however,  chiefly  with  the  "mechanics 
^  Man  and  the  Earth,  New  York  (Duffield),  1906,  p.  62. 


Sec.  2]         is   THE    PRICE    LEVEL   CONTROLLABLE  ?  325 

of  bimetallism"  and  not  its  influence  on  price  levels. 
We  have  now  to  note  the  claim  of  advocates  of  a 
bimetallic  standard  that  such  a  standard  would  tend 
to  steady  prices.^  As  we  have  seen,  by  connecting  the 
currencies  of  both  gold  and  silver  countries,  bimet- 
allism, as  long  as  it  continues  in  working  order,  has 
the  effect  of  spreading  any  variation  of  one  particular 
metal  over  the  combined  area  of  gold,  silver,  and  bime- 
tallic countries.  If  variations  occur  simultaneously  in 
both  metals,  they  may  be  in  opposite  directions,  and 
neutralize  each  other  more  or  less  completely;  while, 
even  if  they  happen  to  be  in  the  same  direction,  the 
combined  effect  on  the  whole  world  united  under  bi- 
metallism would  be  no  greater  than  on  the  two  halves 
of  the  world  under  silver  and  gold  monometallism  re- 
spectively. Even  if  bimetallism  did  not  enlarge  the 
monetary  area,  it  might  reduce  monetary  fluctuations. 
Thus  a  world-wide  gold  standard  might  prove  more 
variable  than  bimetallism.^  But  if  the  amount  of  one 
metal  used  in  coinage  increases  faster  or  more  slowly 
than  business,  while  the  amount  of  the  other  maintains 
a  constant  ratio  to  business,  then  the  use  of  the  two 
metals  results  in  less  steadiness  than  would  result  from 
the  less  variable  of  the  two,  though  in  somewhat  more 
steadiness  than  would  result  from  the  use  of  the  more 
variable. 

Two  variable  metals  joined  through  bimetallism 
may  be  likened  to  two  tipsy  men  locking  arms.  To- 
gether they  walk  somewhat  more  steadily  than  apart, 
although  if  one    happens    to    be   much  more    sober 

*  See  Jevons,  Investigations  in  Currency  and  Finance,  London 
(Macmillan),  1884,  pp.  331-333. 

*Cf.  F.  Y.  Edgeworth,  "Thoughts  on  Monetary  Reform," 
(British)  Economic  Journal,  September,  1895,  p.  449. 


326       THE    PURCHASING   POWER  OP  MONEY       (Chap.  XIII 

than  the  other,  his  own  gait  may  be  made  worse  by 
the  union. ^ 

The  table  in  the  footnote  shows  that  in  the  seven- 
teenth and  nineteenth  centuries  the  two  metals  were 
about  equally  unsteady.  In  the  eighteenth  century 
gold  was  the  more  steady.  During  the  first  half  of  the 
nineteenth  century  silver  was  the  more  steady,  while 
for  1851-1890  gold  was  the  more  steady.  Since  then, 
silver  has  been  the  more  steady.  On  the  whole,  there 
is  not  much  to  choose  between  the  behaviors  of  the  two. 

Bimetalhsm,  then,  even  could  it  be  maintained,  would 
offer  but  an  indifferent  remedy  for  the  variations  in  the 
price  level,  and,  moreover,  there  is  always  the  objection 
previously  noted  that  the  system  may  break  down. 
We  then  saw  that  whatever  the  ratio  at  which  both 
metals  are  to  circulate,  one  metal  is  Hkely,  sometime,  to 
be  produced  in  such  abundance  as  completely  to  fill 
the  money  reservoir,  driving  the  other  metal  altogether 
out  of  circulation.  Such  a  result  may  be  long  in  com- 
ing, but  eventually  it  is  practically  sure  to  come. 

1  The  variabilities  of  gold  and  silver  production  have  been  calcu- 
lated by  one  of  my  students,  Mr.  Morgan  Porter.  He  finds  the 
following  mean  percentage  variations  from  the  mean  productions  for 
each  period  named  :  — 


Gold 

SiLVBH 

1601-1701    5  periods  of  20  years  each 

1701-1800    5  periods  of  20  years  each 

1801-1900    5  periods  of  20  years  each 

% 

7.8 
15.6 
69.0 

% 

7.7 
27.4 
67.0 

1801-1850    5  periods  of  10  years  each 

1851-1885    7  periods  of    5  years  each 

1886-1890    5  periods  of    1  year  each 

1891-1895    5  periods  of    1  year  each 

1896-1900    5  periods  of    1  year  each 

1901-1905    5  periods  of    1  year  each 

52.4 
8.1 
5.9 
13.3 
12.3 
10.7 

22.3 

40.8 

10.5 

6.3 

3.4 

1.9 

Sec.  2]         IS   THE    PRICE    LEVEL   CONTROLLABLE  ?  327 

A  more  important  objection  remains  to  be  noted. 
Since  bimetallism,  as  usually  proposed,  would  greatly 
overvalue  one  of  the  two  metals,  the  first  great  effect 
of  its  adoption  might  be  not  to  steady  prices  but  to 
disrupt  them  and  upset  the  relation  of  debtor  and 
creditor.  While  the  great  overvaluation  of  one  metal 
is  not  a  necessary  feature  of  bimetallism,  it  has  always 
been  the  feature  which  has  made  it  politically  popular. 
Thus,  the  bimetallism  advocated  in  the  United  States 
during  the  last  twenty  or  thirty  years  has  been  a  bimet- 
allism which  would  grossly  overvalue  silver.  It  pro- 
posed that  16  ounces  of  silver  should  circulate  as  the 
equivalent  of  an  ounce  of  gold,  when  during  much  of 
this  time  it  really  required  30  or  35  ounces  of  silver  to 
be  equivalent  to  one  of  gold.  Such  an  overvaluation 
of  silver  would  mean  that  silver  would  be  imported 
from  Mexico,  India,  China,  and  other  silver  countries, 
as  well  as  mined  in  larger  quantities  and  coined  in  the 
United  States,  thus  depreciating  the  currency  both 
greatly  and  suddenly.  The  proposal  was  well  satirized 
by  a  cartoon  in  the  "free  silver"  campaign  of  1896 
representing  the  United  States  as  a  ship  sailing  over 
Niagara  Falls  in  order  to  reach  smooth  sailing  below 
the  falls,  —  if  only  it  survive  the  shock  of  the  fall ! 

Bimetallism  is  the  only  scheme  of  steadying  the 
monetary  standard  which  has  ever  secured  political 
momentum;  and  even  its  popularity  lay  far  less  in  its 
potency  for  ultimately  steadying  than  in  its  potency 
for  immediately  unsteadying  the  standard.  We  now 
pass  on  to  consider  schemes  which  have  never  reached 
the  stage  of  practical  proposals,  but  are  still  wholly 
academic. 

The  first  is  polymetallism,  a  generalization  of  bimet- 
allism.    The  theory  of  bimetallism  contemplates  the 


328       THE    PURCHASING   POWER   OF  MONEY       [Chap,  XIIl 

circulation  side  by  side  of  two  metals;  that  of  poly- 
metallism  looks  to  the  contemporaneous  circulation  of 
more  than  two.  So  long  as  several  metals  could  be 
maintained  in  circulation  together,  the  price  level  might 
fluctuate  less  than  if  one  metal  only  were  used.  But 
all  of  the  theoretical  objections  against  bimetallism 
apply  also  against  polymetalhsm.  One  metal  would 
eventually  drive  all  the  others  out  of  a  country,  or, — 
if  polymetalhsm  were  international,  —  into  the  arts. 

§3 

Recognizing  the  force  of  the  arguments  against  bi- 
metalhsm  (and  polymetalhsm).  Professor  Marshall  has 
suggested  as  a  substitute  a  system  which  has  been  called 
symmetalhsm.  Under  ttiis  scheme  —  symmetallism  — 
two  (or  more)  metals  would  be  joined  together  physically 
in  the  same  coin  or  in  "linked  bars."  Evidently  any 
ratio  could  be  used,  and  neither  metal  could  push  the 
other  out  of  circulation.  The  value  of  the  composite 
coin  would  be  the  sum  of  the  values  of  its  two  constit- 
uents, and  the  fluctuations  in  its  value  would  be  the 
mean  of  the  fluctuations  of  its  constituents.^ 

Many  other  schemes  for  combining  metals  have  been 
suggested.  Among  them  are  the  "joint-metallisms"  of 
Stokes  and  Hertzka,  which  are  kinds  of  bimetallism  at 
a  variable  instead  of  at  a  fixed  ratio.  Another,  advo- 
cated by  Walras,^  is  the  gold  standard  with  a  "silver 
regulator,"  which  is  simply  the  limping  standard  such 
as  now  prevails  in  the  United  States,  France,  or  India 

'See  F.  Y.  Edgeworth,  "Thoughts  on  Monetary  Reform," 
(British)  Economic  Journal,  September,  1895,  p.  448. 

2 "  Monnaie  d'or  avec  billon  d'argent  regulateiir,"  Revue  de  droit 
international,  December,  1884  ;  reprinted  in  Etudes  d' Economie 
politique  appliquee,  Lausanne  (Rouge),  1898,  pp.  3-19. 


Sec.  3]        IS  THE    PRICE   LEVEL   CONTROLLABLE  ?  329 

except  that  the  quantity  of  silver  in  circulation,  instead 
of  being  fixed,  would  be  systematically  manipulated  by 
the  government  in  such  a  manner  as  to  keep  prices 
steady.  But  these,  like  symmetallism  and  bimetallism, 
offer  a  remedy  which  at  best  is  only  partial.  For  in- 
stance, in  Walras's  scheme,  in  order  to  maintain  prices, 
the  amount  of  silver  might  need  to  be  reduced  to  zero 
—  after  which  no  further  regulation  would  be  possible; 
or  it  might  need  to  be  increased  so  far  as  to  expel  all 
gold,  after  which  the  system  would  be  no  longer  a  gold 
standard,  but  would  become  an  inconvertible  silver 
standard.  Worst  of  all,  every  one  of  these  proposed 
remedies  would  be  subject  to  the  danger  of  unwise  or 
dishonest  political  manipulation. 

It  is  true  that  the  level  of  prices  might  be  kept  almost 
absolutely  stable  merely  by  honest  government  regula- 
tion of  the  money  supply  with  that  specific  purpose  in 
view.  One  seemingly  simple  way  by  which  this  might 
be  attempted  would  be  by  the  issue  of  inconvertible 
paper  money  in  quantities  so  proportioned  to  increase 
of  business  that  the  total  amount  of  currency  in  circu- 
lation, multiplied  by  its  rapidity,  would  have  the  same 
relation  to  the  total  business  at  one  time  as  at  any 
other  time.  If  the  confidence  of  citizens  were  pre- 
served, and  this  relation  were  kept,  the  problem  would 
need  no  further  solution. 

But  sad  experience  teaches  that  irredeemable  paper 
money,  while  theoretically  capable  of  steadying  prices, 
is  apt  in  practice  to  be  so  manipulated  as  to  pro- 
duce instability.  In  nearly  every  country  there  exists  a 
party,  consisting  of  debtors  and  debtor-like  classes, 
which  favors  depreciation.  A  movement  is  therefore 
at  any  time  possible,  tending  to  pervert  any  scheme  for 
maintaining  stability  into  a  scheme  for  simple  inflation. 


330       THE   PURCHASING   POWER   OF  MONEY       [Chap.  XIII 

As  soon  as  any  particular  government  controls  a  paper 
currency  bearing  no  relation  to  gold  or  silver,  excuses 
for  its  over-issue  are  to  be  feared. 

Even  if,  in  times  of  peace,  these  persistent  pleas  for 
inflation  could  be  resisted,  it  is  doubtful  if  they  could 
be  resisted  in  time  of  war.  In  time  of  war  many 
plausible  defenses  can  be  given,  notably  the  need  of 
government  supphes.  The  history  of  our  own  country 
in  this  respect  is  not  reassuring.  It  is  natural,  there- 
fore, that  such  schemes  should  have  gotten  in  bad 
odor.  Indeed,  their  odor  has  been  so  bad  that  many 
have  impulsively  concluded  that  the  "quantity  theory" 
which  has  been  appealed  to  as  making  possible  govern- 
ment manipulation  of  prices  must  be  fundamentally 
unsound.  Experience  has  shown,  however,  that  the 
evil  feared  need  not  always  be  realized, 
i  Another  method  by  means  of  which  government  could 
theoretically  keep  the  price  level  more  stable  is  by 
confining  the  primary  money  to  a  precious  metal,  say 
gold,  and  regulating  the  quantity  of  this  metal  in  the 
currency  by  means  of  a  system  of  seigniorage.  Thus, 
as  the  supply  of  gold  from  the  mines  increased,  and 
gold  tended  to  depreciate  in  value,  the  value  of  gold 
coin  could  be  kept  up  by  making  a  continuously  higher 
charge  for  coinage,  in  the  shape  of  seigniorage.  This 
charge  would  become  higher  as  gold  bullion  became 
cheaper,  in  such  proportion  as  to  keep  the  currency  in 
the  same  relation  with  the  volume  of  business,  and  thus 
to  keep  the  level  of  prices  stable.  If,  later,  the  annual 
production  of  gold  should  become  very  small,  and  gold, 
in  consequence,  should  begin  to  appreciate  in  value, 
stability  might  be  maintained  by  a  reversal  of  this 
pohcy,  i.e.  by  gradually  reducing  the  seigniorage  so 
as  to  prevent  appreciation  of  the   currency.     There 


Sec.  3]        IS  THE   PRICE   LEVEL   CONTROLLABLE  ?  331 

would,  however,  be  a  Kmit  to  the  power  to  regulate  in 
this  direction  similar  to  the  hmit  we  noted  in  the  case 
of  Walras's  scheme.  The  seigniorage  could  never  be 
reduced  to  less  than  zero.  Money  can  never  be  ma- 
terially cheaper  than  the  metal  composing  it,  since  the 
slightest  tendency  in  this  direction  will  result  in  coin 
being  exported  or  melted  into  bullion.  In  a  period  of 
rising  prices,  regulation  would  be  easy ;  in  a  period  of 
falling  prices,  regulation  might  be  quite  impossible.^ 

Another  plan  is  a  convertible  paper  currency,  the 
paper  to  be  redeemable  on  demand,  —  not  in  any  re- 
quired weight  or  coin  of  gold,  but  in  a  required  pur- 
chasing power  thereof.  Under  such  a  plan,  the  paper 
money  would  be  redeemed  by  as  much  gold  as  would 
have  the  required  purchasing  power.  Thus,  the  amount 
of  gold  obtainable  for  a  paper  dollar  would  vary  in- 
versely with  its  purchasing  power  per  ounce  as  com- 
pared with  commodities,  the  total  purchasing  power 
of  the  dollar  being  always  the  same.  The  fact  that  a 
paper  dollar  would  always  be  redeemable  in  terms  of 
purchasing  power  would  theoretically  keep  the  level  of 
prices  invariable.  The  supply  of  money  in  circulation 
would  regulate  itself  automatically.  Should  money 
tend  to  increase  fast  enough  to  impair  its  purchasing 
power,  the  notes  would  be  presented  for  redemption 
in  gold;  for  under  the  arrangement  assumed,  the  gold 

^  For  the  effect  of  the  legal  prohibition  of  exportation  see  Kem- 
merer,  Money  and  Credit  Instruments  in  their  Relation  to  General 
Prices,  2d  Edition,  New  York  (Holt),  1909,  p.  39  n.  Cf.  Kemmerer, 
"  The  Establishment  of  the  Gold  Exchange  Standard  in  the  Philip- 
pines," in  the  Quarterly  Journal  of  Economics.  Vol.  XIX,  600-605 
(August,  1905)  ;  Second  Annual  Report  of  the  Chief  of  the  Division 
of  Currency,  etc.,  14,  15,  21-28;  and  "A  Gold  Standard  for  the 
Straits,"  II,  in  the  Political  Science  Quarterly.  Vol.  XXI,  p.  665-677 
(December,  1906). 


332       THE    PURCHASING    POWER  OF  MONEY       [Chap.  XIII 

which  would  be  given  would  always  have  the  same 
purchasing  power.  Should  the  money  tend  to  become 
scarce  and  thus  to  appreciate,  the  amount  of  gold  hav- 
ing unchanged  purchasing  power  would  be  exchanged 
for  the  notes. 

It  is  true  that  this  scheme,  like  a  simple  paper-money 
scheme,  would  be  liable  to  abuse,  —  but  it  would  have 
two  practical  advantages.  Having  a  metallic  basis,  it 
would  inspire  more  confidence  than  a  pure  paper-money 
plan,  while  it  would  offer  less  excuse  for  abuse  and  less 
chance  to  delude  the  public.  Every  change  in  the 
weight  of  the  gold  dollar  would  be  definitely  measurable, 
and  would  have  to  be  justified  to  the  pubhc.  A  reduc- 
tion in  weight  not  fully  explained  by  a  fall  in  prices 
would  be  a  clear  confession  of  depreciation. 

§4 

The  next  plan  to  be  considered  is  that  advocated  by 
Professor  Marshall  and  the  Committee  of  the  British 
Association.^  It  is,  in  essence,  the  revival  of  the  tabu- 
lar standard  proposed  and  discussed  by  Lowe,^  Scrope,' 
Jevons,^  and  others;  a  standard  which  is  relatively  in- 
dependent of  special  legislation.  This  involves  the 
passing  of  a  law  —  first  merely  permissive  —  by  which 
contracts  could  be  expressed  in  terms  of  an  index  num- 
ber. Such  a  law  would  not  be  necessary,  but  it  might 
serve  to  draw  attention  to  the  index  method.      The 

^  See  Report  of  the  British  Association  for  the  Advancement  of 
Science,  1890,  p.  488,  containing  a  draft  of  a  proposed  Act  of  Par- 
liament for  this  purpose. 

2  Present  State  of  England  in  regard  to  Agriculture,  Trade,  and 
Finance.     London,  1622. 

'  Principles  of  Political  Economy,  London,  1833,  p.  406. 

*  Investigations  in  Currency  and  Finance,  London  (Macmillan), 
1884,  p.  122  ;  also  Money  and  the  Mechanism  of  Exchange,  London, 
(Kegan,  Paul),  1893,  Ch.  XXV. 


Sec.  4]        is  THE    PRICE   LEVEL   CONTROLLABLE  ?  333 

money  of  the  country  would  continue  to  be  used  as  a 
medium  of  exchange  and  as  a  measure  of  value,  but 
not  as  a  standard  for  all  deferred  payments.  The 
standard  of  deferred  payments,  when  advantage  was 
taken  of  the  law,  would  be  the  index  number  of  general 
prices;  and  contracts  involving  deferred  payment  could, 
when  desired,  call  for  the  exchange  of  a  given  purchas- 
ing power,  or  of  an  amount  of  money  varying  directly 
with  the  index  number.  To  facilitate  such  a  change, 
it  might  be  well  for  the  government  to  inaugurate  an 
authorized  system  of  index  numbers,  but  government 
action  would  not  have  to  go  farther  than  this,  or  in- 
deed, necessarily,  so  far.  The  aim  would  no  longer  be 
to  keep  the  level  of  prices  absolutely  stable.  Gold  or  sil- 
ver or  both  would  furnish  the  primary  money,  and  their 
value  would  consequently  fluctuate  with  that  of  the  con- 
stituent metal  or  metals.  But  the  contracts  based  on 
index  numbers  would  not  be  affected  because  made 
in  terms  of  the  index  number.  Doubtless  the  plan 
would  encounter  much  opposition,^  but  it  would  ap- 
peal strongly  to  certain  classes.^  For  instance,  those 
''living  on  their  incomes"  would  like  to  be  guaranteed 
a  stable  purchasing  power.  A  widow,  or  a  trustee, 
or  other  long-time  investor,  would  prefer  to  buy  bonds 
which  guaranteed  a  regular  yearly  purchasing  power  over 
subsistence,  rather  than  those  which  merely  promised  a 
given  sum  of  money  of  uncertain  value.  A  few  prece- 
dents already  exist,  suggestive,  at  least,  of  what  the  new 
system  would  be.  In  England,  the  ''tithe  averages" 
have  been  made  to  vary  with  the  value  of  grain,  so  that 
the  tithe  was  in  effect  so  much  grain,  not  so  much  money ; 

1  Cf.  Francis  Walker,  Money,  New  York  (Holt),  1891,  pp.  157-163. 

2  See   Joseph    French   Johnson,    Money   and    Currency,    Boston 
(Ginn),  1906,  p.  175. 


334       THE    PURCHASING   POWER   OP  MONEY       [Chap.  XIII 

also  the  Scotch  fiars  prices  have  existed  for  more  than 
two  centuries  for  similar  purposes,  establishing  the  price 
of  grain  on  the  basis  of  which  rents  contracted  in  grain 
should  be  paid  in  money. ^ 

As  has  been  already  indicated,  government  action 
looking  to  this  result  need  not  necessarily  be  i  taken. 
The  beginnings  of  such  a  plan  for  "a  tabular  standard 
of  value"  could  be  made  at  any  time  by  private  con- 
tracting parties,  some  index  number  already  in  vogue, 
such  as  Sauerbeck's  or  the  Bureau  of  Labor's,  being 
used  as  a  standard.  Should  the  results  of  such  experi- 
ments, on  the  whole,  satisfy  the  contracting  parties, 
others  might  follow  their  lead.  At  first  contracts 
would  be  interpreted  as  having  been  made  in  terms 
of  money  except  when  otherwise  provided.  A  specific 
proviso  would  therefore  be  required  in  contracts  made  in 
terms  of  the  index  number.  If  the  latter  form  of  con- 
tract should  become  more  general,  however,  legislation 
could  be  passed,  making  the  index  number  the  standard 
in  all  cases,  except  where  specifically  provided  that 
payment  should  be  based  on  a  different  standard. 

It  is  to  be  noted  that  such  a  custom,  however  general 
it  might  become,  would  not  do  away  with  the  desir- 
ability of  having  an  elastic  currency  to  respond  to 
seasonal  variations  of  business.  Seasonable  readjust- 
ments of  wages,  for  instance,  and  of  many  other  prices, 
are  difficult.  Custom  tends  to  establish  standards  hold- 
ing through  successive  seasons.  Since  there  is  more 
business  at  some  seasons  than  others,  there  will  be  an 
element  of  strain  unless  there  is  also  an  expansion  of 
credit.  An  elastic  banking  system,  facilitating  credit- 
expansion,  would,  therefore,  remain  a  desideratum. 

^  See  Edgeworth,  Reports  of  the  British  Association  for  the  Ad- 
vancement of  Science  for  1888,  p.  182. .' 


Sec.  4]         is  THE   PRICE   LEVEL   CONTROLLABLE  ?  335 

The  system  of  making  contracts  in  terms  of  the  price 
level  is  not  intended  directly  to  prevent  fluctuations 
in  price  level.  Its  purpose  is  rather  to  prevent  these 
fluctuations  from  introducing  a  speculative  element  into 
business.  But  an  incidental  result  of  the  system  would 
be  that  fluctuations  in  the  level  of  prices  would  be  less 
than  before,  because  credit  cycles  would  no  longer  be 
stimulated.  The  alternate  abnormal  encouragement 
and  discouragement  of  loans  would  cease.  Hence,  credit 
fluctuations  would  become  less,  and  the  level  of  prices 
would  be  comparatively  unaffected  by  them.^  Even  if 
panics  should  occur,  accompanied  by  sharp  falls  of  prices, 
they  would  not  be  as  severe  as  now.  At  present,  loans 
must  be  liquidated  in  terms  of  a  given  amount  of  money, 
though  that  money  may  buy  more  (or  less)  at  the  time 
of  liquidation  than  when  the  loan  was  contracted,  and 
though  the  borrower  must  dispose  of  more  (or  less)  com- 
modities to  raise  the  given  amount.  He  is  compelled  to 
pay,  when  prices  have  fallen,  on  the  same  basis  in  terms 
of  money,  and  a  much  higher  value  in  terms  of  goods, 
than  when  prices  ranged  higher.  Hence  failure  often 
results,  credit  currency  contracts  still  further  because 
of  the  general  distrust,  and  depression  becomes  more 
severe.  With  payment  in  terms  of  purchasing  power, 
the  situation  would  be  altogether  different.  Falling 
prices  would  neither  injure  borrowers  nor  benefit  lenders. 

On  the  whole,  the  "tabular  standard"  seems  to  have 
real  merit.^  Certainly  there  could  be  no  material  harm 
in  trying  a  "permissive "  law.  But  the  tabular  standard 
is  subject  to  serious  if  not  fatal  objections :    One  is  the 

^  See  Jevons,  Money  and  the  Mechanism  of  Exchange,  London 
(Kegan  Paul),  1893,  p.  333. 

2  See  J.  Allen  Smith,  "  The  Multiple  Money  Standard,"  Annals  oj 
the  American  Academy  of  Political  and  Social  Science.     March,  1896. 


336       THE    PURCHASING   POWER   OF  MONEY       [Chap.  XIII 

fact  that  it  would  involve  the  trouble  of  translating 
money  into  the  tabular  standard  and  would  therefore 
fail  to  attract  the  public  sufficiently  to  warrant  its  com- 
plete adoption  by  any  government.  Another  objection 
is  that  its  halfway  adoption  would  really  aggravate 
many  of  the  evils  it  sought  to  correct,  and  therefore 
discourage,  rather  than  encourage,  its  further  extension. 
Even  were  the  system  adopted  in  its  complete  form  for 
any  one  country,  it  would  have  the  disadvantage  of 
isolating  that  country  commercially,  and  thus  reintro- 
ducing the  inconveniences  of  an  uncertain  rate  of  inter- 
national exchange.  An  analogous  inconvenience  would 
arise  by  its  partial  adoption  in  any  one  country.  Busi- 
ness men  naturally  and  properly  prefer  a  uniform  system 
of  accounts  to  two  systems  warring  with  each  other. 
They  would  complain  of  such  a  double  system  of  ac- 
counts in  exactly  the  same  way,  and  on  exactly  the  same 
grounds,  as  they  have  always  complained  of  the  double 
system  of  accounts  involved  in  international  trade  be- 
tween gold  and  silver  countries.  A  business  man's 
profits  constitute  a  narrow  margin  between  receipts  and 
expenses.  If  receipts  and  expenses  could  both  be  reck- 
oned in  the  tabular  standard,  his  profits  would  be  more 
stable  than  if  both  were  reckoned  in  money.  But  if  he 
should  pay  some  of  his  expenses,  such  as  interest  and 
wages,  on  a  tabular  basis,  while  his  receipts  remained 
on  the  gold  basis,  his  profits  would  fluctuate  far  more 
than  if  both  sides,  or  all  items  of  the  accounts,  were  in 
gold.  In  fact,  his  expected  profits  would  often  turn  into 
losses  by  a  slight  deviation  between  the  two  standards, 
in  precisely  the  same  way  as  the  importer  or  exporter  of 
goods  between  China  and  the  United  States  may  have 
his  profits  wiped  out  by  a  slight  variation  in  the  ex- 
change.    In  either  case,  he  would  prefer  to  have  the 


Sec.  5]         is   THE    PRICE   LEVEL   CONTROLLABLE  ?  337 

same  standard  on  both  sides  of  the  account,  even  if  this 
standard  fluctuated,  rather  than  have  two  standards, 
only  one  of  which  fluctuated;  for  his  profits  depend 
more  on  the  parallelism  between  the  two  sides  of  his  ac- 
count than  on  the  stability  of  either.  It  was  to  escape 
the  evils  from  having  two  standards  that,  after  lengthy 
debate  and  experiment,  the  present  gold-exchange  stand' 
ard  was  adopted  in  India,  the  Philippines,  Mexico, 
Straits  Settlement,  Siam,  and  Panama. 

§5 

The  mention  of  the  gold-exchange  standard  brings 
us  to  the  proposal  which  is  here  tentatively  suggested,  — • 
a  proposal  M'hich,  it  is  believed,  may  one  day  be  found 
both  practicable  and  advisable.  This  plan  involves  a 
combination  of  the  tabular  standard  with  the  principles 
of  the  gold-exchange  standard. 

We  have  already  described  briefly  the  gold-exchange 
standard,  and  given  references  to  other  and  fuller 
sources  of  information.  While  the  gold-exchange  stand- 
ard purports  to  be  a  system  of  redemption,  or  partial 
redemption  in  gold  of  the  native  coin,  yet  as  a  matter 
of  fact,  no  gold  is  necessarily  required  in  the  country 
itself  where  the  system  is  in  operation.  Thus,  the 
Philippine  government  does  not  offer  gold  for  silver 
pesos,  even  when  gold  is  wanted  for  export  to  New 
York.  Instead,  it  keeps  a  reserve  of  gold  in  New 
York,  and  "redeems"  the  Filipino's  pesos  in  merely  a 
draft  upon  this  gold.  As  this  draft  may  be  forwarded 
to  New  York,  it  serves  the  purpose  of  gold  redemption 
for  export.  The  price  of  the  sale  includes  a  premium 
on  exchange  corresponding  to  the  usual  excess  above 
the  "gold  point";  that  is,  the  government  charges  the 
Filipino  the  equivalent  of  freight,  insurance,  and  other 
expenses  on  gold  to  New  York. 


338       THE    PURCHASING   POWER   OF   MONEY       [Chap.  XIII 

It  will  be  evident  that  the  gold-exchange  system  is 
only  nominally  a  redemption  system.  In  actual  fact, 
it  is  a  system  of  manipulating  the  silver  currency  in  such 
a  manner  as  to  prevent  its  value  from  diverging  from 
par  with  gold  by  more  than  the  usual  premiums  on 
exchange  between  gold  countries.  This  manipulation 
consists  in  contracting  the  currency  when  the  rate  of 
exchange  reaches  a  certain  point  above  par,  and  ex- 
panding the  currency  when  it  reaches  a  certain  point 
below  par.  The  contraction  of  the  currency  is  secured 
by  selling  foreign  bills  of  exchange  and  locking  up  the 
currency  received  therefor,  while  the  expansion  of  the 
currency  is  secured  by  releasing  this  currency  to  circula- 
tion, or,  if  necessary,  by  coining  more  currency. 

The  successful  operation  of  the  system  is  not  only 
compatible  with,  but  actually  requires,  an  overvalua- 
tion of  the  metallic  content  of  the  silver  currency.  In 
fact,  in  the  Philippines  it  was  found  necessary  to  reduce 
the  silver  pesos  from  374  grains  to  247  grains,  to  prevent 
their  disappearance.  Without  a  margin  between  the 
coin-value  and  the  bullion-value  of  the  peso,  the  power 
to  regulate  its  circulation  would  exist  only  in  one  direc- 
tion—  contraction;  with  such  a  margin,  the  power 
exists  to  expand  as  well  as  to  contract. 

After  once  becoming  familiar,  the  system  would 
operate  just  as  successfully  if  the  weight  of  the  silver 
coins  were  still  further  reduced,  or,  in  fact,  if  a  paper 
currency  were  substituted  instead.  It  will  be  seen, 
therefore,  that  at  bottom  the  gold-exchange  standard  is 
practically  the  same  standard  as  that  which  is  now  in 
operation  for  paper  currency  in  Austria.  In  that 
country  the  paper  is  really  irredeemable,  but  is  kept 
at  par  by  the  sale  of  exchange  on  London. 

The  plan  by  which  the  buUion  content  of  the  coins 


Sec.  51        IS   THE   PRICE   LEVEL   CONTROLLABLE?  339 

is  kept  below  their  value  as  coins  not  only  prevents 
melting  and  exportation,  and  the  consequent  loss  of 
control  of  their  quantity  and  value,  but  also  has  the 
advantage  of  economy.  The  reduction  of  the  weight 
of  the  pesos  was,  in  fact,  used  as  a  means  of  defraying 
the  expense  of  maintaining  the  gold  reserve  and  the 
other  expenses  of  inaugurating  and  operating  the 
system  in  the  Philippines. 

The  gold-exchange  standard  was  at  first  regarded 
with  great  suspicion,  and  its  advocates  scarcely  dared 
claim  for  it  any  better  virtue  than  that  of  a  practical 
makeshift,  affording,  as  it  did,  a  means  of  easy  transi- 
tion from  the  previously  existing  system  to  the  gold 
standard,  without  shock,  or  introducing  an  unfamiliar 
coinage. 

But  the  results  have  been  so  satisfactory  that  it 
may  well  be  asked  whether  those  who  devised  the 
gold-exchange  standard  did  not  build  better  than  they 
knew.  While  the  system  bears  a  close,  though  some- 
what superficial,  resemblance  to  a  fiat  money  system, 
it  has  now  little  or  none  of  the  odium  or  suspicion 
attached  to  it  which  we  associate  with  that  name. 
So  simple  are  the  duties  of  maintaining  the  gold- 
exchange  par,  and  so  unfailingly  has  the  system  been 
faithfully  executed,  that  even  those  who  at  first  most 
strenuously  opposed  it  seem  now  inclined  to  trust  it 
implicitly.  There  is,  indeed,  no  reason  why,  under 
almost  any  conceivable  circumstances,  there  should  be 
€ven  the  fear  of  this  system  being  abused. 

Now  that  there  has  been  actually  constituted  a  new 
form  of  governmental  machinery,  which  can  be  as  fully 
trusted  to  perform  its  functions  of  regulation  as  the 
mint,  there  seems  to  be  no  reason  why  the  system 
should  not  be  extended.     It  is  well  known  that  the  par  of 


340       THE    PURCHASING   POWER   OF   MONEY        [Chap.  XIII 

exchange  which  has  been  adopted  for  the  gold-exchange 
standard  is  quite  arbitrary,  and  it  must  be  evident  that 
this  par  could  be  changed.  The  par  of  exchange  be- 
tween the  English  and  Indian  system  is  16<i.  per  rupee. 
This  par  could  be  easily  changed  to  15c?.  or  17 d.,  and 
gradually  changed  further  in  either  direction.  By  such 
changes  of  the  gold  par  of  exchange,  the  currency  of 
those  countries  now  having  a  gold-exchange  standard 
could,  if  desired,  be  kept  at  par  with  a  tabular  stand- 
ard. Thus,  when  it  is  found  practicable  to  measure 
by  index  numbers  the  exact  shifting  of  the  gold  stand- 
ard, a  corresponding  shifting  of  the  par  of  exchange  or 
price  of  rupees  in  gold  could  be  effected. 

As  the  system  is  now  operated,  the  coinage  is  manip- 
ulated to  keep  it  at  par  with  gold,  that  is,  to  follow  the 
fluctuations  of  the  gold  standard  wherever  they  may 
lead.  We  have,  therefore,  the  spectacle  of  India,  and 
other  countries  formerly  having  a  silver  standard,  now 
clinging  to  the  skirts,  as  it  were,  of  the  gold  standard 
countries,  and  following  that  erratic  standard  where- 
ever  it  may  lead  them,  although  it  is  within  their  power, 
by  exactly  the  same  machinery,  to  keep  their  course 
steady. 

I  would  not,  however,  for  a  moment  suggest  that  these 
countries  should  give  up  their  par  of  exchange  with  gold 
standard  countries.  Although  much  might  be  said  in 
favor  of  such  a  course,  it  would,  to  a  large  extent,  be  a 
step  backward  by  again  restoring  the  uncertainties  of 
international  exchange  which  have  been  mentioned. 
What  is  needed  is  to  induce  the  entire  civilized  world 
to  do  what  is  now  within  the  power  of  the  gold-exchange 
countries  to  do,  viz.  to  keep  pace  with  a  tabular  stand- 
ard. It  is  a  little  anomalous  that  these  gold-exchange 
standard  countries  now  have  a  power  to  regulate  their 


Sec.  5]        IS   THE    PRICE   LEVEL   CONTROLLABLE  ?  341 

price  level,  which  is  not  possessed  by  the  gold  standard 
countries  themselves.  The  latter  are,  by  their  present 
system,  kept  absolutely  at  the  mercy  of  the  accidents 
of  gold  mining  and  metallurgy,  while  the  former  can 
keep  or  change  the  par  of  exchange  with  gold  countries 
at  will. 

But  evidently  the  gold  countries  could  do  precisely 
what  the  silver  countries  have  done,  namely,  inaugu- 
rate the  system  of  a  gold-exchange  standard  by  closing 
their  mints  to  gold,  reducing,  if  need  be,  the  weight  of 
gold  coins  (although  with  the  depreciation  now  going 
on  in  gold,  this  would  probably  not  be  necessary), 
and  operating  an  exchange  standard  system  in  pre- 
cisely the  same  way  that  the  Phihppines  and  the  other 
countries  mentioned  now  operate  their  gold-exchange 
system. 

To  make  this  clear  we  shall  suppose,  at  first,  that  one 
country,  say  Austria,  would  continue  on  the  gold  stand- 
ard while  England,  Germany,  France,  the  United  States, 
and  the  other  chief  countries  of  the  world  should  close 
their  mints  to  the  free  coinage  of  gold.  They  could 
then  maintain  a  gold-exchange  standard  with  a  (vary- 
ing) par  of  exchange  with  Austria.  By  suitably  chang- 
ing the  par  of  exchange  from  time  to  time,  the  whole 
commercial  world,  excepting  Austria,  could  then  keep 
the  purchasing  power  of  money  stable,  instead  of  allow- 
ing it  to  fluctuate  with  gold.  The  same  relation  which 
India  now  bears  toward  England  would  then  be  held 
by  both  India  and  England  toward  Austria.  But 
it  would  not  even  be  necessary  that  one  country  like 
Austria  should  hold  aloof  in  commercial  isolation.  The 
system,  when  put  in  operation,  should  include  all  the 
countries  concerned  and  sufficiently  interested  to  enter 
into  a  treaty  agreement.     Instead  of  sacrificing  its  own 


342        THE    PURCHASING   POWER   OF  MONEY       [Chap.  XIH 

interests  by  serving  as  a  gold  standard  country  in 
terms  of  which  all  the  other  countries  of  the  world 
should  in  common  adjust  their  pars  of  exchange, 
Austria  could  itself  adjust  its  currency  by  buying  and 
selling  gold.  In  other  words,  precisely  the  same  prin- 
ciples which  regulate  the  currency  of  India  or  the 
Philippines,  by  buying  and  selling  exchange  on  gold 
abroad,  could  be  operated  more  directly  through  buying 
and  selling  gold  itself  at  home.  Austria  might  be  a 
good  country  in  which  to  do  this,  because  it  has  long 
operated  substantially  this  system,  and  by  it  kept  its 
irredeemable  paper  money  at  a  fixed  par  with  gold. 
Should  suitable  treaty  arrangements  be  effected, 
Austria  might  maintain  a  par,  not  with  a  fixed  weight 
of  gold,  but  with  such  a  weight  of  gold  as  should  have  a 
fixed  purchasing  power,  and  could  do  this  by  buying 
and  selling  gold  at  these  adjusted  prices,  selling  gold 
bullion  for  gulden  to  contract  the  currency,  and  buying 
gold  bullion  for  gulden  to  expand  the  currency.  All 
other  countries  could  maintain  their  par  with  Austria, 
or  each  other,  by  the  methods  by  which  now  India 
maintains  its  par  with  England,  or,  if  they  chose,  by 
exactly  the  same  process  as  proposed  for  Austria.  In 
fact,  it  is  evident  that  the  method  of  maintaining  par 
by  selling  exchange  on  other  countries,  and  by  exchang- 
ing currency  directly  for  some  commodity,  such  as 
gold,  are  at  bottom  much  the  same  thing. 

In  order  that  such  an  international  system  should 
work,  we  might  imagine  three  separate  functions : 
(1)  the  function  of  maintaining  an  exchange  par  with 
the  Austrian  gulden  to  be  performed  by  Foreign  Ex- 
change Offices  exactly  as  at  present  in  the  Philippines 
under  the  gold-exchange  system;  (2)  the  similar  func- 
tion of  regulating  the  currency  in  at  least  one  country, 


Sec.  5]        IS  THE   PRICE   LEVEL   CONTROLLABLE  ?  343 

say  Austria,  by  a  Bureau  of  Currency  Regulation 
through  buying  or  selhng  gold,  at  the  option  of  the 
pubUc,  at  an  official  price,  changing  from  time  to  time 
according  to  the  decisions  of  the  Statistical  Office  about 
to  be  mentioned;  (3)  the  function  of  fixing  this  official 
price  of  gold  according  to  the  price  level.  An  inter- 
national Statistical  Office  at,  say.  The  Hague,  could  be 
estabUshed  to  do  this  in  a  purely  clerical  manner;  its 
duties  would  consist  in  ascertaining  the  index  number 
of  prices  in  the  usual  way  and  then  dividing  the 
market  price  of  gold  by  that  number. 

For  instance,  if,  a  year  after  the  system  was  started, 
it  were  found  by  the  Statistical  Office  that  prices  had 
risen  one  per  cent,  this  Office  would,  in  order  to  neutral- 
ize the  rise,  issue  an  official  declaration  to  the  Bureau 
of  Currency  Regulation  fixing  the  official  price  of  gold 
at  substantially  one  per  cent  lower  than  the  ruling 
market  price.  At  this  cheap  price  the  public  will  buy 
gold  bullion  of  the  government  and  surrender  currency 
in  return.  Therefore  the  currency  will  be  contracted 
and  general  prices  will  fall  until  no  more  gold  is  called 
for,  or  until  there  is  declared  a  new  official  gold  price. 
Should  the  next  official  gold  price  be  set  above  the 
market  price,  the  government  would  become  a  buyer 
of  gold  and  would  thus  reissue  some  of  the  currency 
previously  called  in,  or  if  need  be,  issue  new  currency. 

The  plan,  as  above  outlined,  fixes  a  single  price  of  gold 
at  which  the  government  must  be  ready  either  to  buy 
or  sell.  There  would  be  practical  advantages,  however, 
in  fixing  a  pair  of  prices  differing  slightly  from  each 
other,  the  higher  for  selling  and  the  lower  for  buying. 
The  device  of  a  pair  of  prices  was  proposed  by  Ricardo.* 

^  Proposals  for  an  Economical  and  Secure  Currency,  2d  Edition, 
London  (Murray),  1816,  p.  26. 


344       THE    PURCHASING   POWER  OF  MONEY       [Chap.  XIII 

It  is  also  employed,  as  we  have  seen,  in  the  gold-exchange 
standard  to  simulate  the  "gold-points."  The  Austrian 
paper  currency,  although  usually  called  irredeemable,  is 
kept  at  par  with  gold  by  a  similar  arrangement  under 
which  the  Austro-Hungarian  bank  stands  ready  to  buy 
gold  at  k.  3,  278  ^  per  kilo  and  to  sell  gold-exchange  on 
London  at  a  sHghtly  higher  rate. 

It  will  be  seen  that  the  plan  here  proposed  requires 
no  revolution  of  the  world's  currencies.  It  requires  Ut- 
tle  more  than  to  assemble,  into  one  working  whole, 
operations  already  existing  separately,  viz.  (1)  cal- 
culating Index  Numbers  as  done  at  present  by  our 
Bureau  of  Labor;  (2)  buying  and  selHng  exchange,  as 
done  at  present  by  the  PhiUppine  Government;  (3) 
buying  and  selling  gold,  as  done  at  present  in  Austria; 
(4)  periodically  readjusting  the  gold  pars  as  was  done 
at  least  once  when  the  present  system  was  inaugurated 
in  India,  the  Philippines,  Panama  and  Mexico.  The 
readjustment  of  par  is  the  only  feature  which  could  be 
called  new,  and  this  should  not  be  condemned  as  caus- 
ing fluctuations  in  values;  for  its  only  object  is  to  prevent 
the  fluctuations  from  which  we  now  suffer.  Neither 
this  periodic  readjustment  nor  any  other  feature  of  the 
plan  would  require  changes  in  the  circulating  medium. 
Each  nation  would  continue  to  use  its  old  familiar  cur- 
rency, whether  gold,  silver,  or  paper.  The  ordinary 
man  would  be  unaware  of  any  change. 

The  cost  of  maintaining  the  gold-exchange  system  has 
been  slight  and  the  cost  of  maintaining  the  system  here 
proposed,  whatever  it  might  be,  could  be  as  nothing 
compared  with  the  benefits  it  would  render  the  entire 
civilized  world. 

^  See  L.  V.  Mises,  "  The  foreign  exchange  policy  of  the  Austro- 
Hungarian  Bank,"  Economic  Journal,  June,  1909,  p.  201. 


Sec.  5]  IS  THE    PRICE   LEVEL   CONTROLLABLE  ?  345 

One  incidental  benefit  which  could  easily  be  secured 
would  be  the  oft-proposed  readjustment  of  relative 
values  of  various  coins;  for  the  first  adjustment  of  pars 
would  naturally  make  the  sovereign  equivalent  to  five 
dollars,  the  ruble  to  fifty  cents,  the  Japanese  yen  to 
fifty  cents,  the  Dutch  florin  to  forty  cents,  the  mark 
to  twenty-five  cents,  the  franc  to  twenty  cents,  the 
Austrian  crown  to  twenty  cents,  and  the  Portuguese 
crown  to  ten  cents. 

The  plan  as  above  outlined  contemplates  the  regu- 
lation of  the  world's  currencies  by  buying  and  selling 
gold;  but  of  course  silver  or  any  other  commodity 
could  be  used  instead.  The  less  variable  the  commod- 
ity relatively  to  commodities  in  general,  the  less  would 
be  the  readjustments  needed  and  the  less  active  the 
buying  or  selling  of  that  commodity  by  the  govern- 
ment. 

The  objections  which  could  be  urged  against  this  sys- 
tem are  doubtless  many,  but  they  do  not  seem  to  be  as 
serious  as  the  objections  which  have  already  been  urged 
against  the  adoption  of  the  gold-exchange  standard, 
and  which  have  been  satisfactorily  answered  by  the 
course  of  events.  In  fact,  there  would  seem  to  be  no 
greater  danger  in  trusting  Austria,  under  treaty  agree- 
ment, to  maintain  her  gulden  at  an  ideal  par  with  com- 
modities in  accordance  with  an  index  number,  than  to 
trust  her,  as  at  present,  to  maintain  stable  exchange 
with  London,  or  than  to  trust  the  Indian,  Mexican, 
Panama  or  PhiHppine  governments  to  maintain  their 
overvalued  silver  at  par  with  gold.  The  functions  in- 
volved are  clerical;  the  acts  required  are  specific.  De- 
partures from  a  strict  compliance  with  the  law  or  treaty 
would  be  instantly  recognized,  and  would  bring  upon 
the  culprit  wrath  and  punishment  proportionate  to  the 


346       THE   PURCHASING   POWER   OF   MONEY       [Chap.  XIII 

international  gravity  of  the  offense.  The  plan  does  not 
require  and  would  not  permit  any  experimental  dosing 
of  the  circulation  dependent  on  the  judgment  of  an 
official.  The  official  who  regulates  does  so  merely  by 
buying  and  selling  at  specific  prices  fixed  by  others; 
and  he  must  buy  or  sell  at  the  pleasure  of  the  public. 
He  would  have  no  more  choice  than  a  broker  who  is 
ordered  to  buy  or  sell  at  prices  specified  by  his  custom- 
ers, or  than  his  prototype,  the  present  official  in  the 
Phihppines,  who  now  buys  or  sells  foreign  exchange. 
The  danger  of  abuse  or  fraud  in  the  Statistical  Office, 
the  work  of  which  is  based  on  published  market  prices 
and  is  necessarily  done  in  the  light  of  day,  would  seem 
negligible. 

Not  only  would  the  scheme  seem  to  be  entirely  free 
from  the  possibility  of  mismanagement  by  individual 
officials,  but  it  would  seem  also  to  be  fully  safeguarded 
against  the  danger  of  inflationistic  legislation.  No  in- 
dividual nation  could  inflate  the  currency  without 
withdrawing  from  the  international  arrangement  and 
isolating  itself  accordingly,  while  it  is  quite  inconceiv- 
able that  all  the  civilized  nations  of  the  world  should 
voluntarily  and  simultaneously  commit  the  folly  of 
inflationistic  legislation. 

But,  before  any  control  of  the  price  level  be 
undertaken,  the  public  must  learn  to  realize  its  neces- 
sity. So  long  as  the  rank  and  file  even  of  business 
men  fail  to  realize  that  they  are  daily  gambling*  in 
changes  in  the  value  of  money,  a  fact  of  which  they 
are  blissfully  unaware,  they  will  exert  no  demand  for 
preventing  those  changes.  They  are  the  parties  whose 
interests  are  chiefly  involved,  and  the  first  essential 
step  in  the  reform  process  is  that  they  shall  be  made 
to   comprehend  the   benefits   of   a  stable   purchasing 


Sec.  6]         is  THE    PRICE   LEVEL   CONTROLLABLE?  347 

power.^    Until  this  time  arrives,  any  political  proposals 
will  be  premature. 

§6 

At  the  beginning  of  this  chapter  we  reviewed  the 
principles  determining  the  purchasing  power  of  money 
and  the  practical  problems  involved.  We  then  consid- 
ered the  possible  methods  of  avoiding  the  evils  of  varia- 
bility in  purchasing  power.  Among  these,  one  of  the 
most  feasible  and  important  was  found  to  be  an  increase 
of  knowledge,  —  both  specific  knowledge  of  conditions 
and  general  knowledge  of  principles.  Next,  the  claims 
of  bimetallism  and  polymetallism  as  means  of  maintain- 
ing a  stable  level  of  prices  were  considered.  It  was  seen 
that  there  was  no  guarantee  of  keeping  two  or  more 
metals  in  circulation  indefinitely  at  an  agreed  ratio,  and 
it  was  pointed  out  that,  even  could  this  be  done,  the 
gain  in  stability  of  prices  would  be  likely  to  be  incon- 
siderable. The  latter  objection  was  brought  also 
against   symmetallism — the    proposal    to    have   more 

^  A  recent  popular  pamphlet  by  A.  C.  Lake,  Currency  Reform  the 
Paramount  Issue,  Memphis  (28  N.  Front  St.),  Tenn.,  proposes  to 
stop  the  free  coinage  of  gold.  As  I  write,  other  evidences  of  the 
spread  beyond  academic  circles  of  the  idea  that  gold  is  an  unstable 
standard  come  to  hand.  The  rapid  rise  in  the  cost  of  living  has  of 
course  thrust  the  subject  on  the  attention  of  the  magazine  and  news- 
paper press.  Mr.  Edison,  in  a  recent  interview,  predicts  the  further 
downfall  of  gold,  through  the  discovery,  —  sure  to  be  made  sooner 
or  later,  —  of  cheap  methods  of  extracting  immense  quantities  of  gold 
from  some  Southern  clays.  He  asks  the  pertinent  question  :  "  Is  it 
not  absurd  to  have,  as  our  standard  of  values,  a  substance,  the  only 
real  use  of  which  is  to  gild  picture  frames  and  fill  teeth?"  Mr. 
Carnegie,  in  his  last  gift  of  ten  millions  of  dollars  to  the  Carnegie 
Institution  of  Washington,  stipulates  that  a  certain  part  of  the  in- 
come shall  be  set  aside  as  a  sinking  fund  against  "  the  diminishing 
purchasing  power  of  money."  This  is  significant  as  one  of  the  first 
cases  in  which  a  business  man  has  taken  cognizance,  in  a  practical 
way,  of  the  instability  of  gold. 


348      THE    PURCHASING    POWER   OF  MONEY         [Chap.  XIII 

than  one  precious  metal  in  each  standard  coin  —  as 
well  as  against  joint  metallism,  etc. 

Several  methods  were  next  considered  by  which  a 
government  might  regulate  the  quantity  of  money  rel- 
atively to  business  so  as  to  keep  the  level  of  prices  con- 
stant. One  such  method  was  to  make  inconvertible 
paper  the  standard  money,  and  to  regulate  its  quantity. 
Another  was  to  regulate  the  supply  of  metallic  money 
by  a  varying  seigniorage  charge.  Still  another  was  to 
issue  paper  money,  redeemable  on  demand,  not  in  fixed 
amounts  of  the  basic  precious  metal,  but  in  varying 
amounts,  so  calculated  as  to  keep  the  level  of  prices 
unvarying.  Lastly  was  considered  the  proposal  of  the 
writer,  —  to  adopt  the  gold-exchange  standard  combined 
with  a  tabular  standard. 

It  was  suggested  that  the  first  step  in  this  needed 
reform  would  be  to  persuade  the  public,  and  especially 
the  business  public,  to  study  the  problem  of  monetary 
stability  and  to  realize  that,  at  present,  contracts  in 
money  are  as  truly  speculative  as  the  selling  of  futures, 
—  are,  in  fact,  merely  a  subdivision  of  future-selling. 

The  necessary  education  once  under  way,  it  will  then 
be  time  to  consider  schemes  for  regulating  the  purchas- 
ing power  of  money  in  the  light  of  public  and  economic 
conditions  of  the  time.  All  this,  however,  is  in  the 
future.  For  the  present  there  seems  nothing  to  do 
but  to  state  the  problem  and  the  principles  of  its 
solution  in  the  hope  that  what  is  now  an  academic 
question  may,  in  due  course,  become  a  burning  issue. 


For  a  fuller  explanation  of  the  above  described  plan 
to  "  standardize  the  dollar,"  the  reader  is  referred  to 
pages  494  ff. 


APPENDIX  TO  CHAPTER  II 

§  1  (to  Chapter  II,  §  3) 

The  Concept  of  an  Average 

The  subject  of  averages  or  means  is  so  important  —  both 
theoretically  and  practically  —  and  so  little  upon  it  is  readily 
available  for  economic  readers  that  a  short  statement  of  its 
fundamental  principles  may  be  fitly  inserted  here.^ 

There  are  numerous  kinds  of  averages  or  means.  Among 
them  are  the  arithmetical,  geometrical,  and  harmonical ;  and 
of  each  of  these  there  are  many  different  varieties.  The 
simple  arithmetical  mean  of  a  specific  series  of  terms  is  found 
by  adding  the  terms  together  and  dividing  by  their  number. 
Thus,  suppose  it  is  desired  to  find  a  mean  of  2  and  8.     It  is 

evidently  ^    ~J'    '  =  — -  =  5.     This  is,  as  a  matter  of  fact,  the 

mean  most  commonly  employed. 

The  simple  geometrical  mean  is  obtained  by  multiplying  all 
the  terms  together  and  extracting  that  root  of  the  product 
which  corresponds  to  the  number  of  terms.  Thus,  the  geo- 
metrical mean  of  2  and  8  is  V2  X  8  or  4. 

The  simple  harmonical  mean  of  any  number  of  terms  is 
the  reciprocal  of  the  arithmetical  average  of  their  reciprocals. 
1_ 


For  2  and  8  it  is  t-t-t  or  3^ 


2 

The  weighted  arithmetical  mean  is  a  modification  of  the 
simple  arithmetical  mean.  Suppose  it  is  desired  to  find  the 
mean  height  of  two  groups  of  trees,  one  tall,  the  other  short. 

^  For  discussion  of  certain  statistical  averages,  see  Dr.  Franz 
Zizek,  Die  Statistischen  Mittelwerte,  Leipzig  (Duncker  &  Humblot), 
1908,  in  which  (p.  2)  will  be  found  further  references. 

349 


350         THE    PURCHASING   POWER   OF  MONEY      [Append.  H 

The  tall  group  is  8  yards  high,  the  short,  2.  The  simple 
arithmetical  mean  as  we  have  seen  is  5.  But  this  mean  treats 
both  groups  as  of  equal  importance.  Let  us  suppose  that 
there  are  twenty  of  the  two-yard  trees  and  ten  of  the  eight- 
yard  trees,  and  let  us  seek  a  mean  of  the  two  heights,  such 
as  will  give  equal  importance  to  each  tree.  This  will  give 
the  short  group  of  twenty  trees  twice  the  importance  of  the 
tall  group  of  ten  trees.  We  shall  be  giving  equal  importance 
to  each  tree  if  we  take  the  simple  arithmetical  mean  of  the 
thirty  trees.  But  this  simple  mean  of  thirty  trees  will  be  a 
weighted  mean  of  the  two  groups  of  trees.  It  is  to  be  found 
by  adding  their  heights  together  (twenty  heights  of  two 
yards  plus  ten  of  eight)  and  dividing  by  the  number  of  trees 

(20  +  10).     That  is,  the  mean  height  is  20  X  2  +10X8  ^  . 
K      -r      J  ,  6  20+10  ' 

and  this  (considered  as  an  average  of  the  two  groups  instead 
of  that  of  the  thirty  trees)  is  said  to  be  the  weighted  arith- 
metical mean  of  2  and  8,  the  2  being  weighted  twenty  times, 
and  the  8,  ten  times.  The  weighted  mean  of  the  two  groups 
means  the  simple  mean  of  the  thirty  trees.  In  other  words 
when  we  "  weight "  the  various  terms  averaged,  we  no  longer 
count  these  terms  once  each,  but  we  count  one  term  as  though 
it  were  (say)  twenty,  and  another  as  though  it  were  (say) 
ten  and  the  number  of  times  we  count  a  term  is  its  "  weight." 
In  the  same  way  we  may  define  the  weighted  geometrical 
and  weighted  harmonical  means.  Taking  the  same  example 
of  the  trees,  we  find  the  results  to  be  respectively  V22°  •  8^° 

°'  ^-^^^  ^^^  20(^)  1 10(1)  ^^  2|. 
30 

The  same  results  would  have  been  obtained  in  each  case 
if,  instead  of  the  weights  20  and  10,  we  had  taken,  as  weights, 
2  and  1. 

Since  there  are  so  many  different  kinds  of  means,  the  ques- 
tion arises,  What  is  the  meaning  of  an  average  or  mean  in  gen- 
eral ?  We  answer  :  Any  mean  of  a  series  of  terms  must  be 
obtainable  from  them  by  a  mathematical  rule  such  that, 


Sec.  1]  APPENDIX  TO  CHAPTER  II  351 

when  applied  to  a  series  of  identical  terms,  it  will  make  their 
mean  identical  with  each  of  them.  Any  rule  of  averaging  is 
admissible  which  is  consistent  with  this  condition  (that  the 
average  of  identical  terms  must  be  identical  with  each). 
We  know  that  the  simple  arithmetical  mean  A,  of  a,  b,  and  c 

is  A  =  •     It  is  easy  to  see  that  this  formula  meets 

o 

the  required  test.     Substituting  A   for  each   of  the  three 

n-X-h  -I-  c  A    \    A    \    A 

magnitudes  a,  b,  and  c  in       '       '     ,  we  obtain  — — — — — , 

o  o 

which  is  evidently  equal  to  A  ;  thus  the  test  is  satisfied. 

Again,  let  G  be  the  geometrical  mean  of  a,  b,  and  c ;  so 
that  G=wabc.  This  formula  also  conforms  to  the  defini- 
tion of  a  mean  because  G  =  VGGG. 

Similarly,  the  harmonical  average  (which  we  may  call  H) 

of  a,  b,  and  c'ls  H=  - — - — j  •     This  also  conforms,  because 
a     0     c 


1  +  1  +  1 
H     H     H 


3 

For  a  weighted  arithmetical  average  A  to  of  a,  b,  c,  the 

weights  being  a  /3,  y,  we  have  the  formula  A«,  = —     \,  ~r  Y'^ 
which  conforms  to  our  test,  since  evidently 
.  _aAy,-\-(3Ay,-\-yAy,_ 

By  applying  this  general  rule,  we  can  make  at  will  in- 
numerable kinds  of  averages.  It  is  only  necessary  to  write 
any  formula  twice, .  once  using  the  terms  to  be  averaged 
and  once  using,  instead,  the  required  average,  and  then 
equate  the  two.     Thus,  let  us  take  the  complicated  formula 

(a  +  a^  +  Ka')(b+j^ 

3^^ •     This  may  be  employed  to  obtain  a 

c-f- v6c 


it  with  the  similar  form  .-= •     That  x  as 

■5/     o 


352  THE  PURCHASING   POWER   OF  MONEY      [Append.  II 

new  species  of  average  {x)  of  a,  b,  and  c,  simply  by  equating 

(x  +  x^-{-Kx^)(x-\-^^ 

x-{-Vx^ 

determined  by  this  equation  will  conform  to  our  definition  of 
an  average  is  evident,  since  substituting  x  for  a,  h,  and  c, 
the  equation  becomes  a  truism,  showing  that  the  proposed 
new  average  of  the  identical  terms  a;  is  a:. 

A  special  case  of  the  definition,  requiring  particular  men- 
tion, is  that  in  which  two  or  more  means  (not  necessarily  of 
the  same  kind)  are  related  to  one  another.  In  order  that 
A  should  be  a  mean  of  ai,  02,  as,  •••  when  we  know  that  B  is 
a  mean  of  61,  62,  bz,  ••■  it  is  only  necessary  to  have  a  deter- 
mining formula  such  that  if  ai  =  02  =  Ui  •••  and  at  the  same 
time  61  =  62  =  63  •  •  •  (each  of  which  by  hypothesis  must  be 
equal  to  B),  then  A  shall  also  be  equal  to  each  of  the  magni- 
tudes Gi,  (h,  as,  etc.  Many  examples  of  pairs  of  means  Uke 
A  and  B  will  be  given  in  Chapter  X  (on  the  construction  of 
index  numbers).     The  following  is  a  simple  example  :  — 

Let  nAB  =  aybi  -\-  0262  +  «3&3  H and  let  B  be  the  arithmeti- 
cal mean  =           ^       ^    —    (n  being  the  number  of  terms). 
n 

Then  A  is  a.  (new)  sort  of  mean  of  ai,  a^,  as;  for,  substituting 
A  for  ai,  02,  as,  •••  and  B  for  61,  62,  bs,  in  the  equation  nAB 
—  fli&i  +  •••,  the  equation  is  satisfied. 

§  2  (to  Chapter  II,  §  5) 

The  Concept  of  Velocity  of  Circulation 

The  velocity  of  circulation  of  money  has  been  defined  as  a 
ratio  of  the  money  expended  to  the  average  money  on  hand, 
that  is,  as  a  rate  of  turnover.  A  rate  of  turnover  differs  from 
the  popular  concept  of  velocity.  The  latter  regards  velocity 
as  the  average  number  of  times  money  changes  hands  from 
one  person  to  another  ;  whereas,  the  concept  we  have  em- 
ployed treats  velocity  as  the  average  number  of  coins  which 


Sec.  21  APPENDIX  TO   CHAPTER   II  353 

pass  through  one  man's  hands,  divided  by  the  average  amount 
held  by  him.  The  difference  between  the  two  concepts  is 
very  similar  to  that  between  two  methods  of  obtaining  the 
velocity  of  a  railway  train.  One  method  is  to  follow  the 
train  for  a  certain  number  of  miles,  and  note  how  long  a  time 
it  takes  to  travel  those  miles.  The  other  is  to  stand  on  a 
certain  spot  beside  the  track  and  note  the  time  consumed  by 
a  given  length  of  train  in  passing  that  spot.  Following  the 
train  from  place  to  place  is  like  following  a  coin  from  person 
to  person,  while  watching  the  train  pass  one  point  is  like  ob- 
serving the  rate  of  turnover  of  one  person's  purse.  We  may 
distinguish  the  two  methods  as  the  "  coin-transfer  "  method 
and  the  ''  person-turnover  "  method.  Both  methods,  if  cor- 
rectly employed,  yield  the  same  result.  But  in  the  coin-trans- 
fer method,  an  important  distinction  is  usually  overlooked, 
the  distinction  between  the  gross  and  net  circulation  of  money. 
What  is  desired  is  the  rate  at  which  money  is  used  for  pur- 
chasing  goods,  not  for  "  making  change."  The  result  is  the 
difference  between  the  number  of  times  each  piece  changes 
hands  against  goods,  and  the  number  of  times  it  changes 
hands  with  goods.  If  a  $10  bill  is  transferred  in  purchase  of 
goods  and  $2  is  given  back  "  in  change,"  the  actual  money 
expended  for  goods  is  measured,  not  by  S12,  the  gross  trans- 
fer of  money,  nor  yet  by  $10,  the  gross  amount  transferred 
against  goods,  but  by  $8,  the  net  amount  paid  for  goods. 

If  it  is  desired  .n  the  coin-transfer  method,  to  learn  the 
average  velocity  x  circulation  of  two  pieces  of  money,  such 
as  a  dollar  and  a  ten-cent  piece,  we  must  not  only  find  the 
net  rate  of  turnover  of  each  coin,  but  also  take  account  of 
the  discrepancy  between  the  buying  efficiencies  of  the  two 
coins.  Let  it  be  assumed  that  during  the  year  the  dollar  is 
passed  115  times  against  goods  and  15  times  with  goods,  so 
that  its  net  velocity  of  circulation  is  115  —  15  or  100.  If  we 
suppose  the  velocity  of  the  ten-cent  piece  to  be  290  —  90  or 
200,  the  average  velocity  of  the  two  must  somehow  take 
account  of  the  different  values  of  different  denominations. 
A  dollar  is  the  equivalent  of  ten  dimes.  Its  rapidity  of  cir- 
2a 


354         THE   PURCHASING   POWER   OF  MONEY      [Append.  II 

culation  should  therefore  be  "weighted"  tenfold  in  order 

to  get  the  real  average,  that  is,  the  average  of  the  service 

performed  by  the  two.     The  net  rate  of  circulation  of  100 

for  the  dollar  is  equivalent  to  a  net  velocity  of  circulation 

of  100  for  each  and  every  one  of  ten  dimes.     It  follows  that 

XI                        1     •*       f  +u    +           .       •    lOX  100  +  200 
the  average  velocity  of  the  two  coms  is  ' ,  a 

result  much  closer  to  the  velocity  of  the  dollar  than  to  that 
of  the  dime.  With  these  two  safeguards  against  error  ap- 
plied to  the  coin-transfer  method,  it  is  easy  to  see  that  the 
coin-transfer  method  will  yield  the  same  results  as  the  per- 
son-turnover method.^ 

There  is  yet  another  magnitude  which  should  be  considered 
in  connection  with  the  velocity  of  monetary  circulation. 
This  may  be  called  the  average  time  of  turnover,  i.e.  the 
average  amount  of  time  consumed  by  all  the  given  money, 
in  being  turned  over  once.  This  is  the  "  reciprocal "  of 
velocity.  If  money  changes  hands  twenty  times  in  a  year, 
it  turns  over,  on  the  average,  once  in  ^V  of  a  year,  or  once  in 
somewhat  over  18  days.  This  is  its  average  time  of  turnover. 
If  the  average  velocity  of  circulation  or  rate  of  turnover  is 
forty  times  a  year,  then  the  average  time  of  turnover  is  ^  of 
a  year  or  about  9  days.  Or,  instead  of  considering  all  the 
given  money  directly,  let  us  come  at  it  through  a  component 
part  of  it.  If  a  man  having,  on  the  average,  $10  in  his 
pocket  every  day,  expends  on  the  average  $1  a  day,  he  evi- 
dently turns  over  yjj  of  his  money  each  day.  Since  to  turn 
over  yV  of  tiis  average  stock  each  day  is  to  turn  over  the 
whole  of  it  36|^  times  a  year  or  once  in  10  days,  the  time  of 
turnover  will  be  10  days.  If  the  man  under  consideration 
had  a  pocketbook  arranged  with  a  series  of  ten  one  dollar 
bills,  and  every  day,  as  one  was  taken  from  the  top  to  be 
expended,  another  were  added  at  the  bottom,  evidently  any 
and  every  bill  would  remain  in  his  hands  just  ten  days 
traveling  from  the  bottom  to  the  top  of  the  pile. 

*  For  mathematical  statement,  see  §  5  of  this  Appendix. 


Sec.  3] 


APPENDIX   TO   CHAPTER   II 


355 


§  3  (to  Chapter  II,  §  5) 

*^  Arrays  "  of  p's,  Q's,  and  pQ's 
Let  us  assume  that  the  year  is  divided  into  an  indefinite 
number  of  periods,  or  moments,  and  distinguish  the  prices 
and  quantities  relating  to  those  successive  periods  by  the 
subscripts  1,  2,  3,  etc.,  at  the  left ;  and  that  we  are  deaUng 
with  a  community  of  an  indefinite  number  of  persons,  dis- 
tinguished likewise  by  subscripts  at  the  right.  Thus  the 
quantity  of  a  particular  kind  of  goods  purchased  by  individ- 
ual No.  1  in  moment  No.  3  is  represented  by  sQi  and  the  price 
of  the  sale  by  sPi-  The  entire  system  of  quantities  and  prices 
is  represented  by  the  two  following  "  arrays." 


Pkesons 

Periods 

Total 

Persons 

Periods 

Average 

1 

1 

3... 

1 

2 

1 

2 
3 

l9l 

l93 

2qi 

293 

3?1... 
392--- 
3?3-.. 

«3 

1 
2 
3 

lP2 

IPs 

2P\ 
2i)2 
2^3 

zP\--- 

3P2-- 
3i>3... 

P\ 

i>2 

Total 

iQ 

2Q 

zQ 

Q 

Average 

\P 

2P 

ZP.: 

P 

We  have  just  stated  the  meaning  of  the  letters  inside  these 
arrays.  Those  outside  are  as  follows :  Qi  is  the  total  quantity 
bought  by  person  1  and  is  the  sum  dgi  +  2^1  +  3?i  +  •••)  of  all 
quantities  purchased  by  him  in  all  the  different  periods  of  time. 
Like  definitions  apply  to  Q2,  Qs,  etc.  iQ  is  the  total  quantity 
purchased  in  moment  1  and  is  the  sum  (151  +  152  +  153+  •••) 
of  all  quantities  purchased  in  that  moment  by  all  the  differ- 
ent persons.  Like  definitions  apply  to  2Q,  sQ,  •••  Finally 
Q  is  (as  ah-eady  employed  in  the  text)  the  grand  total  of  quan- 
tities bought  by  all  persons  in  all  periods  of  time.    Evidently, 


Q  =  iQ  +  2Q-\-zQ-\-"- 

=  Ql  +  (?2  +  Q3+   - 

=  i^i  +  251  +  etc.  + 152  +  252  +  etc. 


+  etc. 


356 


THE   PURCHASING    POWER   OF  MONEY      [Append.  H 


Like  definitions  apply  to  the  letters  outside  the  p  array,  but 
the  relations  to  the  letters  inside  are  here  averages  instead  of 
sums.  We  may  best  derive  the  form  of  these  averages  from 
a  third  or  intermediate  array  for  -pQ  indicating  the  money 
values  of  the  purchases. 
This  last  named  array  is 


Persons 

Peeiods 

Total 

1 

2 

3 

1 

2 
3 

\P2  1?2 
1^3  153 

2Pl2?l 
2i'2  29-2 
2i53  2?3 

3  Pi  3?1 
3^2  3(/2 
3^3  3^3 

PlQl 
P2Q2 
P3Q3 

Total 

iPlQ 

iP  2§ 

zP  sQ 

pQ 

In  this  array  the  same  relations  must  evidently  hold  as  in 
the  Q  array.  That  is,  pQ,  the  entire  sum  spent  on  the  given 
commodity  by  all  persons  in  the  community  during  all  periods 
of  the  year,  must  be  equal  to  (1)  the  sum  of  the  column  above 
it,  (2)  the  sum  of  the  row  at  its  left,  and  (3)  the  sum  of  the 
interior  terms  of  the  array.  In  other  words,  it  must  be  equal 
to  (1)  the  sum  of  the  total  yearly  amounts  spent  by  the  many 
different  persons,  (2)  the  sum  of  the  total  amounts  spent  in 
the  community  at  the  many  different  periods  of  the  year,  and 
(3)  the  sum  of  the  purchases  of  all  the  individuals  in  all  the 
periods. 

The  nature  of  the  p  array  is  now  determined  by  the  Q  and 
the  pQ  arrays.  It  must  namely  be  such  as  to  permit  the 
summation  just  described  for  the  pQ  array.  That  is,  each  of 
the  average  prices  (such  as  pi)  must  conform  to  the  type  of 
formula:  — 

Pi  Qi  =  iPi  igi  +  2P1 291  +  •••,  that  is 

^  i??i  igi  +  2P1 2<7l  I     ,- 
_  i??i  iQ'i  +  27>i  2<7i  +  ••• 


Sec.  3]  APPENDIX  TO   CHAPTER   II  357 

Hence,  p  is  a  weighted  average  of  ipi,  2P1,  etc.,  the  weights 
being  i^i,  291,  etc.  That  is,  the  average  price  paid  by  person 
No.  1  is  the  weighted  arithmetical  average  of  the  prices  paid 
by  him  at  different  moments  through  the  year,  the  weights 
being  the  quantities  bought.  The  same  principle  obtains  for 
all  other  persons. 

Similarly,  the  average  price,  ip,  may  be  shown  to  be 

iViiqi-^iP2iq2+  ••• 
iQ(=  iqi-\-iq2-\ ) 

That  is,  the  average  price  in  period  No.  1  is  the  weighted 
arithmetical  average  of  all  prices  paid  by  different  per- 
sons at  moment  No.  1,  the  weights  being  the  quantities 
bought  by  each.  The  same  principles  obtain  at  all  other 
moments. 

Finally,  the  average  price,  p,  in  the  lower  right  corner  of 

the  p  array,  is  either  p  =  >.  /     'X  ^  1    ,  ' — r  (that  is,  p  is  a 

weighted  arithmetical  average  of  pi,  p^,  etc.,  the  weights 
being  Q\,  Q2,  etc.) ;  or  (using  the  row  instead  of  column),  p  is 
the  like  weighted  arithmetical  average  of  ip,  2P,  etc.,  the 
weights  being  iQ,  2Q,  etc.;  or  lastly,  either  of  these  two  ex- 
pressions for  p,  combined  with  the  preceding  expression  for 
Vh  P2,  etc.,  or  with  that  for  ip,  2P,  etc.,  may  be  used  to  show 
that  p  is  a  weighted  arithmetical  average  of  all  the  p's 
within  the  array,  the  weights  being  the  corresponding  q's.  In 
short,  the  price  of  each  commodity  for  the  year  is  its  aver- 
age at  all  times  and  for  all  purchases  in  the  year  weighted 
according  to  the  quantities  bought. 

This  principle  covers  the  method  of  averaging  prices  in 
different  localities.  Thus  the  average  price  of  sugar  in  1909 
in  the  United  States  is  the  weighted  arithmetical  average  of 
all  prices  of  sales  by  all  individuals  throughout  the  United 
States,  and  at  all  moments  throughout  the  year,  the  weights 
being  the  quantities  bought.  Thus,  if  there  are  large  local 
or  temporal  variations  in  price,  it  is  important  to  give  chief 
weight  to  the  largest  purchases. 


358  THE    PURCHASING   POWER  OF  MONEY      [Append.  II 

What  has  been  said  as  to  Q  and  p  arrays  relates  only  to 
one  commodity.  But  the  same  principles  apply  to  each  com- 
modity yielding  separate  arrays  corresponding  to  each  of  the 
total  quantities,  Q,  Q',  Q",  etc.,  as  well  as  corresponding  to 
each  of  the  average  prices,  p,  p',  p",  etc. 

§  4  (to  Chapter  II,  §  5) 

"  Arrays  "  of  e's,  m's,  and  Vs 

In  the  preceding  section  we  have  seen  that  there  exists  an 
"  array  "  of  p's,  pQ's  and  Q's  for  each  commodity.  These 
relate  to  the  right  side  of  the  equation  of  exchange.  Similar 
arrays  relate  to  the  left  side. 

If,  as  before,  we  assume  a  community  of  any  number  of 
persons,  distinguished  respectively  by  subscripts  at  the  right, 
and  if  we  divide  the  year  into  moments,  distinguished  by 
subscripts  at  the  left,  we  may  designate  the  amount  of  money 
expended  in  the  first  moment  by  the  first  person  as  iCi,  the 
average  amount  of  money  he  has  on  hand  at  that  moment 
as  iWi  and  his  velocity  of  circulation  at  that  moment  (reck- 
oned at  its  rate  per  year)  as  iFi.  The  expenditure  in  the 
moment  being  iCi,  that  moment's  rate  per  annum  is  iWnei, 
there  being  n  moments  in  the  year,  so  that  the  velocity  of 

circulation  or  rate  of  turnover  per  annum,  iFi,  is  n^-^  •  A 

similar  notation  may  be  used  to  express  the  amounts  ex- 
pended and  held  and  the  velocity  of  circulation  for  each 
member  of  the  community  during  each  moment  of  the 
year  as  shown  in  the  following  three  "  arrays  "  (inside  the 
lines). 

In  the  first  table,  Ei  at  the  right  of  the  first  line  is  the 
sum  expended  by  the  first  person,  being  the  sum  of  iCi, 
261, 3C1,  •  •  •  in  the  first  line  representing  the  amounts  expended 
by  him  at  successive  moments  during  the  year.  Likewise, 
E2  is  the  sum  expended  by  the  second  person  during  the 
year,  and  E3  is  the  sum  expended  by  the  third.  lE  at  the  foot 
of  the  first  column  is  the  amount  expended  by  all  persons  in 


Sec.  4J 


APPENDIX   TO   CHAPTER   II 


359 


the  first  moment ;  that  is,  it  is  the  sum  of  all  the  amounts 
in  the  column  above  it ;  2E  is  likewise  the  amount  expended 
by  all  persons  in  the  second  moment;  3^,  the  amount  ex- 
pended in  the  third,  etc.  Finally,  E,  in  the  lower  right-hand 
corner,  is,  as  employed  in  the  text,  the  grand  total  expended 
by  all  persons  in  all  moments  of  the  year.  Evidently  E  can 
be  obtained  by  adding  the  row  to  the  left  of  it,  or  by  adding 
the  column  above  it.  It  is  also  the  sum  of  all  the  elements 
inside  the  hnes,  i.e.  E  =  'ZiE  =  "ZEy  =  SiCi. 


Amottnt  Expended 


Monet  on  Hand 


Pkbsons 

Periods 

Total 

Persons 

Periods 

AVERAGS 

1 

2 

3... 

1 

2 

3  ••• 

1 

lei 

2*1 

3C1  ••• 

^1 

1 

iVfli 

2n»i 

zm-i  ■■' 

nil 

2 

1«2 

2«2 

3*2  ••• 

^2 

2 

lW»2 

2WI2 

3W2  ••• 

»l2 

3 

1*3 

2«S 

3*3  ••• 

Ez 

3 

Ittlz 

2W3 

3«»3  ••• 

TMa 

— 

— 

— 

— 

— 

— 

— 

— 

Total 

lE 

2-fi 

zE  ••• 

E 

Total 

iM 

iM 

sM- 

M 

Velocity  of  CiRcnLATioN 


Pbbboms 

Periods 

Average 

1 

2 

3 

1 

2 

3 

imi 
im2 

1*3                  TT 

lW»3 

^    2*1               T;r 
"     ^      =2Fl 

2mi 

^   2*2             T^ 
n           =  2  K  2 
2m2 

«  2*3             -p- 

2n»3 

«  3^1             T7- 
"    ^     =8Fl 

8n»i 

«   3*2             TA 
"    »„     =3F2 

3n»2 

"    ^     =8F3 
3WJ3 

nil 

^=F2 

m-z 
^=F, 

Average 

"ri-^ 

^  2-^            jr 
2iH 

„  3^            T;r 

^=F 

In  the  second  table,  M  in  the  lower  right  corner  is  a  sum 
of  the  average  amounts  held   by  the  different  members  of 


360         THE   PURCHASING   POWER   OF  MONEY      [Append.  II 

the  community  during  the  year,  i.e.  it  is  the  sum  of  the 
elements  in  the  column  above  it,  mi,  rrh,  W3,  etc.,  each  of 
which  is  by  hypothesis  a  simple  average  of  the  row  to  its 
left. 

Or,  again,  ilf  is  a  simple  average  of  the  row  to  its  left,  \M, 
zM,  zM,  etc.,  the  average  amounts  of  money  in  the  com- 
munity, in  the  successive  moments  of  the  year,  each  of  which 
averages  is   in  turn  the  sum  of  the  column  above  it,  i.e. 

M  =  'Xmi  =  — — .     Thus  M  is  both  the  sum  of  averages  and 
n 

the  average  of  sums.     That  the  two  are  equal  follows  by 

expressing  both  in  terms  of  the  elementary  quantities  iWi 

by  means  of  the  equations 

mx  =  ^^^+^^^  +  ^^^+-,etc., 
n 

and  the  equations  iM  =  imi  + 1^2  +  1W3  +  •••.  It  is,  of  course^ 
easy  also  to  express  M  directly  in  terms  of  imi,  etc.,  within 

the  table.    Thus  expressed,  it  is  — ^— \ 

n 

The  third  table  (that  for  velocities)  is  derived  from  the 
other  two.  As  just  explained,  i7i  is  the  velocity  of  circula- 
tion (considered  as  a  per  annum  rate)  for  the  first  person  in 
the  community  in  the  first  moment. 

There  remain  to  be  shown  the  relations  of  the  elements  in 
the  V  table. 

Evidently,  F  =  — 

M 

__  Ei-\-  E2-\-  ••• 
'mi-\-mz-\-  ••• 

^miVi-\-nhV2-\-  '"  Qx 

Wi+m2+  ••• 

Form  (1)  shows  that  F  is  a  weighted  average  of  the  yearly 
velocities  of  the  different  persons,  the  velocity  of  each  person 
being  for  the  entire  year  and  weighted  according  to  his  aver- 
age amount  of  money  on  hand. 


Sec.  4]  APPENDIX  TO   CHAPTER   II  361 

Following  an  analogous  but  slightly  different  sequence,  we 
have 

M 

iM  +  zAf  +  - 


n 
\E  -\-  oE  -\-  •" 

—  n 


1M  +  2M  + 


xM{n^]+.M[n^^-\- 


^iMiF  +  2M2y  + 
1M  +  2M+  - 


("fi)_ 

(2) 


Form  (2)  shows  that  V  is  also  the  weighted  average  of  the 
yearly  velocities  of  the  successive  moments  into  which  the 
year  is  divided,  the  velocity  of  each  moment  being  for  the 
entire  community  and  weighted  according  to  its  average 
amount  of  money  then  in  circulation. 

Thus  form  (1)  gives  V  in  terms  of  the  column  above  it, 
while  form  (2)  gives  V  in  terms  of  the  row  at  its  left.  A 
formula  similar  to  (1)  maybe  constructed  to  express  each  of 
the  magnitudes  \V,  2V,  3V,  etc.,  in  terms  of  the  column 
above  it,  while  a  formula  similar  to  (2)  may  be  constructed 
to  express  each  of  the  magnitudes  Fi,  F2,  F3,  etc.,  in  terms 
of  the  row  at  its  left.  That  is,  the  velocity  in  the  entire 
community  at  any  particular  moment  is  a  specific  form  of 
average  of  the  velocities  of  different  persons  at  that  moment; 
and  the  velocity  for  the  entire  year  of  any  particular  person 
is  a  specific  form  of  average  of  the  velocities  at  different 
moments  for  that  person. 

Finally,  F  may  be  expressed,  not  only  as  an  average  of  its 


362         THE   PURCHASING   POWER   OF  MONEY      (Append.  II 

column  and  row  as  in  formula  (1)  and  (2),  but  also  as  an 
average  of  the  magnitudes  in  the  interior  of  the  table.  This 
last  result  may  be  obtained  in  several  ways,  of  which  the 
most  direct  may  briefly  be  expressed  as  follows :  We  know 
that  E  is  the  sum  of  the  interior  of  the  first  or  E  table,  that 

is,  ^  =  Siei;  and  that  M  is  equal  to  -  SiWi.   Hence,  we  have 

n 

V  =  — 
M 


n 


2 
=  n— 


\       xmiJ 


2iWi 

That  is,  V  is  the  weighted  arithmetical  average  of  the  yearly 
velocities  pertaining  to  different  persons  in  different  mo- 
ments, each  velocity  being  weighted  by  the  amount  of  money 
on  hand  in  that  instance.  The  mathematical  reader  will 
perceive  that  an  alternative  treatment  would  derive  the  re- 
sult in  terms  of  an  harmonic  average. 

§  5  (to  Chapter  II,  §  5) 

The  Coin-transfer  Concept  of  Velocity  and  the  Concept  of 
Time  of  Turnover 

We  now  turn  to  the  coin-transfer  concept  of  velocity  of 
circulation.  To  show  what  kind  of  an  average  V  is  of  the 
velocity  of  circulation  of  individual  coins,  or  rather  of  in- 
dividual pieces  of  money  in  general,  let  us  denote  the  values 
of  the  individual  pieces  of  money  circulating  in  the  commu- 
nity by  the  letters  a,h,c,  d,  etc.,  and  let  us  denote  the  net  ve- 
locity of  circulation  of  these  (the  number  of  times  exchanged 


Sec.  5]  APPENDIX  TO   CHAPTER   II  363 

against  goods  minus  the  number  of  times  exchanged  with 
goods  or  "  in  change  ")  by  h,  i,  j,  k,  respectively,  etc.  Then 
E,  the  total  amount  expended,  is  denoted  by  ha  -\-  ih  -\r  jc  -\- 
kd-]-  •••;  and  the  amount  of  money,  M,  in  the  community 
is  a  +  6  +  c  +  d. 

Hence  ^  ^  /^g  +  ^•&  +  jc  +  A:rf^+  '- 

M         a-\-b  +  c  +  d-\-  ■■• 

That  is,  —  is  a  weighted  average  of  the  net  velocities  of  cir- 
culation of  the  different  pieces  of  money,  the  velocity  of  each 
piece  being  weighted  according  to  its  denomination.     But  ■—- 

is  also  V,  which  we  have  already  seen  is  the  velocity  of  circu- 
lation in  the  person-turnover  sense. 

It  is  clear,  therefore,  that  the  coin-transfer  method  of  aver- 
aging is  the  same  in  results  as  the  person-turnover  method, 
if  all  the  pieces  of  money  in  the  community  are  included. 

Finally,  we  come  to  the  concept  of  ''  time  of  turnover." 

If  velocity  of  circulation  is  represented  as  V,  then  —  repre- 
sents the  time  of  turnover.  Similarly,  the  reciprocals  of  iV, 
zV,  •••,  Vi,  V2,  •••,  iFi,  1V2,  •",  2F1,  •••,  are  corresponding  times 
of  turnover.  Using  W  for  the  reciprocal  of  V  and  applying 
the  appropriate  subscripts,  we  may  write  an  array  of  W's 
analogous  to  the  previous  array  of  F's,  and  we  may  show 
that  W  is  an  average  of  Wi,  W2,  or  of  iW,  2W,  ••■  or  of  JVi, 

lW2,-,2Wi,  -. 

But  these  averages  are  all  harmonic  averages.  To  see  this, 
we  need  only  remember  that  V  has  already  been  analyzed  ^ 
as  a  weighted  average  of  the  elementary  F's,  and  that  W  has 
been  defined  as  the  reciprocal  of  V.  That  is,  W  is  the  re- 
ciprocal of  this  weighted  average  of  elementary  F's.  But 
the  elementary  IF's  are  reciprocals  of  the  elementary  F's. 
In  other  words,  W  is  the  reciprocal  of  the  weighted  arith- 
metical average  of  the  reciprocals  of  elementary  W's.     This 

*  In  §  4  of  this  Appendix. 


364  THE    PURCHASING    POWER   OF   MONEY      [Append.  II 

makes  W,  by  definition,  a  weighted  harmonic  average  of 
these  elementary  magnitudes. 

§  G  (to  Chapter  II,  §  5) 
Algebraic  Demonstration  of  Equation  of  Exchange 

It  is  clear  that  the  equation  of  exchange,  MV  =  ^pQ,  is 
derived  from  elementary  equations  expressing  the  equiva- 
lence of  purchase  money  and  goods  bought.  The  money 
expended  by  any  particular  person  at  any  particular  mo- 
ment is,  by  the  very  concept  of  price,  equal  to  the  quanti- 
ties of  all  commodities  bought  in  that  moment  by  that 
person  multiphed  by  the  prices,  i.e. 

\e\  =  ipi  iqi  +  ip'i  iq\  +  ip'\  iq"i  +  •-. 

From  this  equation  and  others  like  it,  for  every  person  in 
the  community  and  for  every  moment  in  the  year,  simply 
by  adding  them  together,  we  obtain,  for  the  left  side  of  the 
equation,  the  sum  of  the  e's  which  we  call  E  ;  and  for  the 
right  side  the  sum  of  all  the  pq's.  We  have  already  seen  in 
the  text  how  the  left  side,  E,  may  be  converted  (by  multiply- 
ing and  dividing  by  M)  into  MV,  and  we  have  also  just  seen 
(§  3  of  this  Appendix)  how  the  sum  of  all  the  terms  relating  to 
each  particular  commodity  represented  on  the  right  side  may 
be  converted  (by  similar  simple  algebraic  operations)  into  one 
term  of  the  form  pQ  so  that  the  whole  sum  becomes  ^pQ. 
The  final  result  is,  therefore,  MV  =  ^pQ.  This  reasoning 
constitutes,  therefore,  a  demonstration  of  the  truth  of  this 
formula,  based  on  the  simple  elementary  truth  that  in  every 
exchange  the  money  expended  equals  the  quantity  bought 
multiplied  by  the  price  of  sale. 

§  7   (to  Chapter  II,  §  5) 

P  must  be  a  Specific  Form  of  Average  in  order  to  vary 
directly  as  M  and  V  and  inversely  as  the  Q's 

Let  us  assume  that  V  and  the  Q's  remain  invariable  while 
M  changes  to  Mo  and  p,  p',  p",  etc.,  to  po,  p'o,  p"o,  etc. 


Sec.  6]  APPENDIX   TO    CHAPTER    II  365 

(The  subscripts  ''  0  "  refer  to  a  year  called  the  base  year 
other  than  the  original  year.)  We  have  for  the  two  years 
respectively  the  two  equations :  — 

Mo7  =  poQ  +  p'oQ'+- 


whence  by  division,  we  obtain 

M     vQ-\-v'Q'+"-     \Po. 


J  \VoJ 


Mo     PoQ  +  p'oQ'  +  -  PoQ  +  p'oQ"  +  - 

The  last   expression  is  evidently  a  weighted   arithmetical 

average  of  (  — ),  f-^l,   etc.,  the  weights  being  poQ,  p'oQ\ 
\PoJ    \poJ 

etc.     We  conclude  that,  if  the  velocity  of  circulation  and  the 

quantities  of  goods  exchanged  remain  unaltered,  while  the 

quantity  of  money  is  altered  in  a  given  ratio,  then  prices  will 

change  in  this  same  ratio  "  on  the  average,"   the  average 

being  exactly  defined  as  a  weighted  arithmetical  average,  in 

which  the  weights  are  the  values  of  goods  sold,  reckoned  at 

the  prices  of  the  base  year.     The  ratio  may  evidently  also  be 

written:  — 

M  ^  pQ  +  p'Q'+-'  ^  1 

Mo     poQ-\-p'oQ'+-     PoQ  +  p'oQ'+  - 

pQ  +  p'Q'-h-\ 
1 

°(^>o+(^°>'o-+- 

PQ  +  P'Q'+'- 

which  is  a  weighted  harmonic  average  of    ^,  -^>  etc.,  in 

Po     Po 
which  the  weights  are  pQ,  p'Q',  etc.,  that  is,  the  values,  not 
in  the  base  year,  but  the  other  year. 

If  M  and  the  Q's  remain  invariable,  while  V  changes  from 

V  to   Vi,  evidently  the  ratio  —  will  be  expressed  by  pre- 

Vi 

cisely  the  same  formulae  as  above. 


366         THE   PURCHASING   POWER  OP  MONEY      [Append.  II 

K  the  Q's  remain  invariable,  while  M  and  V  both  change, 

evidently  the  ratio    -z-rTr  will  be  expressed  by  the  same 
MiVi 

formulae. 

Again  the  same  formulae  apply  if  M  and  V  remain  invari- 
able while  the  Q's  all  vary  in  a  given  ratio,  or  if  the  Q's  all 
vary  in  a  given  ratio  in  combination  with  any  variation  in 
ilf  or  F  or  both.  In  short,  the  formulae  apply  perfectly  in  all 
cases  of  variation,  except  when  the  Q's  vary  relatively  to  each 
other. 

These  formulae,  it  should  be  noted,  are  those  later  discussed 
as  the  formulae  numbered  (11)  in  the  large  table  of  formulae 
in  the  Appendix  to  Chapter  X. 


APPENDIX  TO  CHAPTER  III 

§  1  (to  Chapter  III,  §  2) 

''Arrays"  of  k's  andr's 
Let  k  be  the  ratio  of  deposits  to  money  in  circulation  f  —  j 

which,  on  the  average,  the  public  prefers  to  keep ;  k  will  then 
be  derivable  from  the  like  ratios  for  the  different  persons 
and  business  firms  in  the  community  in  the  successive  mo- 
ments of  the  year,  and  we  may,  therefore,  form  an  array  on 
the  analogy  of  previous  arrays,  of  the  form :  — 


Pekiods 

Pebbons 

AVKEAGK 

1 

2 

1 

1*1 

2*1 

*1 

2 

1*2 

2*2 

*2 

Average 

1* 

2* 

* 

Each  letter  outside  the  array  is  a  weighted  arithmetical  aver- 
age either  of  the  row  to  its  left  or  of  the  column  above  it. 
k  (in  the  lower  right  corner)  also  is  both  of  these  as  well  as 
the  weighted  arithmetical  average  of  all  the  elements  inside 
the  Unes  (the  weights  being  in  all  cases  the  amounts  of  money 
in  circulation,  which  are  the  denominators  of  the  ratios  repre- 
sented in  the  arrays).  The  same  proportions  hold  true  if 
"harmonic"  be  substituted  for  "arithmetic"  (provided  the 
weights  be  changed  from  the  denominators  to  the  numerators 

367 


368        THE    PURCHASING   POWER   OF  MONEY     [Append.  Ill 

of  the  ratios,  viz.  the  deposits) .    These  theorems  can  be  easily 

proved  analogously  to  those  in  §  7  of  the  Appendix  to  Chapter 

M' 
II,  remembering  that  k  = 

Similarly,  we  may  let  r  stand  for  the  average  ratio,  for  the 
year,  of  the  reserves  of  all  banks  (ft)  to  their  deposits  (M'). 

This  ratio  (r,  or  -^j  is  resolvable  into  an  array  expressing 
the  ratios  for  different  banks  at  different  moments,  viz.:  — 


Periods 

AVEKAQE 

1 

2 

1 

iri 

ari 

ri 

2 

1>'2 

2r2 

ri 

Average 

ir 

2r 

r 

Here  each  element  outside  the  lines  is  a  weighted  arithmetic 
(or  harmonic)  average  of  the  terms  in  the  row  to  its  left  or 
the  column  above  it,  while  r  is  both  of  these  as  well  as  a 
weighted  arithmetic  (or  harmonic)  average  of  all  the  terms 
inside,  the  weights  being  (for  the  arithmetic  average)  the 
deposits  in  each  case  or  (for  the  harmonic  average)  the 
money  in  each  case.  The  total  currency  of  the  community 
is  /i+ikf +M',  although  only  M  +  M'  is  actually  in  circulation. 

§  2  (to  Chapter  III,  §  4) 

Algebraic  Demonstration  of  Equation  of  Exchange  Including 
Deposit  Currency 

The  money  expended  for  goods  by  individual  1  at  moment 
1  is  iCi  and  his  check  expenditure  is  le'i.  His  total  expendi- 
ture for  goods  by  money  and  checks  is,  therefore,  iCi  +  le'i  = 


Sec.  2]  APPENDIX  TO   CHAPTER   III  369 

By  adding  together  all  such  equations  for  all  persons  in 
the  community  and  all  moments  of  the  year,  we  obtain  the 
equation 

E+E'  =  %pQ 
which  becomes 

MV -\- M'V  =  :S,pQ 

since,  by  definition,  V  =  tt  and  V  =  —  • 


2s 


APPENDIX  TO  CHAPTER  V 

§  1  (to  Chapter  V,  §  5) 

Effect  of  Time  Credit  on  Equation  of  Exchange 

It  is  important  to  note  that,  though  the  system  of  book 
credit  has  a  great  influence  on  prices  indirectly,  it  does  not 
enter  into  the  equation  of  exchange  hke  circulation  or  bank 
credit.  We  may  properly  include  in  the  discussion  with 
book  credit,  those  cases  of  credit  where  the  record  of  the 
debt  is  not  simply  on  the  books  of  one  of  the  two  parties,  but 
in  which  an  explicit  record  exists  in  the  form  of  a  promissory 
note  given  by  the  purchaser  to  the  seller.  In  either  case, 
goods  are  bought  by  a  promise  to  pay  at  a  later  time ;  in 
the  one  case,  the  promise  is  exphcit ;   in  the  other,  implied. 

Such  an  exchange  of  goods  against  a  later  payment  may 
be  resolved  into  two  successive  exchanges.  The  first  occurs 
at  the  start  when  the  credit  is  given  for  the  goods.  The  pur- 
chaser then  buys  goods  in  exchange  for  a  promise  to  pay. 
The  second  exchange  occurs  at  the  close  of  the  transac- 
tion, when  the  debt  is  Uquidated.  The  original  purchaser 
may  then  be  said  to  buy  back  his  book  credit  or  promissory 
note  with  money.  Unlike  bank  credit,  then,  time  credit 
does  not  directly  save  the  use  of  money.  Its  immediate  effect 
is  simply  to  postpone  ^  that  use,  since,  to  eventually  extin- 
guish the  credit,  as  much  money  or  checks  must  be  expended 
as  though  cash  were  paid  in  the  first  instance.  Dr.  Andrew, 
now  Assistant  Secretary  of  the  Treasury,  points  out  that  if 
time  credit  is  being  contracted  faster  than  it  is  being  ex- 

'  See  A.  Piatt  Andrew,  "Credit  and  the  Value  of  Money,"  Pro' 
ceedings  Seventeenth  Annual  Meeting,  American  Economic  Associa- 
tion, December,  1904. 

370 


Sec.  1]  APPENDIX  TO   CHAPTER   V  371 

tinguished,  prices  tend  to  become  higher,  but  that  as  soon  as 
the  paying  of  these  debts  becomes  as  rapid  as  the  making  of 
them,  prices  will  fall  back  to  their  old  level.^  The  excess  of 
credit  contracted  over  credit  extinguished  acts  just  as  does 
so  much  money  or  bank  deposits  offered  for  goods. 

In  order  to  show  how  these  considerations  as  to  book  credit 
affect  the  equation  of  exchange,  let  us  denote  the  creation  of 
all  book  credits  and  other  time  loans  by  the  letter  E",  and 
their  extinguishment  by  the  letter  E'".  The  left  side  of  our 
equation  of  exchange  —  or  the  total  of  money  payments, 
check  payments,  and  book  charges  and  promissory  notes 
for  goods  bought  in  the  course  of  the  year  —  will  now  be 
MV  -\-  M'V  -\-  E" ;  and  the  right  side,  including  the  value 
of  (1)  goods  bought  and  (2)  debts  maturing  and  extin- 
guished during  the  year  by  payment  of  money  or  check, 
will  be  represented  by  2pQ  -\-  E'".  Transposing  for  con- 
venience £"",  the  equation  of  exchange  may  now  be  written 
MV  +  M'7'  +  E"  -  E'"  =  2pQ.  Since  E"  will  be  approxi- 
mately equal  to  E'",  these  equal  and  opposite  terms  nearly 
cancel,  i.e.  E"  —  E'"  becomes  zero,  and  the  equation  virtually 
becomes  again  MV  -{-  M'V  =  ^pQ. 

Before  leaving  the  subject  it  may  be  noted  that  book  credit 
tends  to  increase  prices  by  creating  offsetting  debts  and  thus 
diminishing  the  volume  of  trade  which  must  be  done  by  money 
or  checks.  Thus,  the  farmer  buys  on  account  at  the  village 
store,  occasionally  selling  farm  produce  there,  also  on  account. 
The  account  is  balanced  at  long  intervals  when  the  difference 
only  is  paid  in  money.'  And,  of  course,  as  pointed  out  in  the 
text  of  this  chapter,  book  credit  tends  also  to  increase 
velocity.' 

» Andrew,  loe.  cit.  » Ihid,  p.  10.  '  Chapter  V,  §  4. 


APPENDIX  TO  CHAPTER  VI 

§  1  (to  Chapter  VI,  §  1) 

Modification  of  Equation  of  Exchange  required  by  Inter- 
national Trade 

We  have  already  seen  that  there  are  two  equations  of  ex- 
change, one  for  purchases,  and  the  other  for  sales.  In  a  closed 
community,  these  two  are  necessarily  identical,  for  every 
purchase  by  one  member  of  the  community  is  a  sale  by  an- 
other member.  But  in  a  community  with  international  trade 
they  will  be  slightly  different.  The  equation  of  exchange  as 
developed  in  this  book  relates  to  the  expenditure  of  money 
for  the  purchase  of  goods,  and  not  to  the  receipt  of  money 
for  the  sale  of  goods.  This  equation  of  exchange  at  its  last 
stage  of  elaboration  was 

MV  +  M'V  +  E"  -  E'"  =  -%pQ 

where  the  letters  have  the  meanings  previously  given  to  them, 
E"  relating  to  the  debts  contracted  in  the  given  period  in 
book  accounts  and  promissory  notes  used  in  purchase  of 
goods,  and  E'"  relating  to  the  extinguishment  of  such  debts 
during  the  same  period.  Since  MV  was  developed  from  E, 
and  M'V  from  E',  this  equation  may  be  written  as  follows:  — 

'      E  +  E'  +  E"-E"'=^p,Q^ 

where  the  letters  E  on  the  money  side  of  the  equations  are 
used  to  indicate  that  the  money  is  expended  money  and  the 
subscripts  h  on  the  goods  side  are  used  to  indicate  that  the 
goods  are  goods  bought ;  likewise,  if  the  letter  R  is  used  to  in- 
dicate received  money,  and  the  subscript  s  to  indicate  that  the 

372 


Sec.  1]  APPENDIX  TO   CHAPTER  VI  373 

goods  are  goods  sold,  the  following  equation  expresses  the  re- 
ceipt of  money,  etc.,  in  exchange  for  the  sale  of  goods:  — 

If  there  is  no  external  trade,  the  several  magnitudes  in  these 
two  equations  will  evidently  be  identical  on  each  side.  If 
external  trade  exists,  each  equation  may  be  resolved  into  an 
equation  in  which  are  distinguished  the  home  trade  and  the 
outside  trade.  Thus,  for  the  first  equation,  relating  to  ex- 
penditures, the  E,  E',  etc.,  may  be  replaced  hyH  -{-0,11'  -\-  0', 
etc.,  where  the  JY's  relate  to  the  purchases  at  home  and  the 
O's  to  money  spent  outward.  On  the  other  side  of  the  equa- 
tion the  SpftQft  may  be  replaced  by  '^pnQh  +  "^piQi  where  the 
subscripts  h  relate  to  the  goods  purchased  at  home  and  the 
subscripts  i  to  those  coming  inward.  The  equation  will  then 
become :  — 

{H  +  H'-{-  H"  -  H'")  +  {0-^0'-\-  0"  -  0'") 

which,  for  brevity,  we  may  write  %H  +  20  =  ^phQh  +  '^ViQu 
Similarly,  the  second  equation,  relating  to  sales,  may  be 
written :  — 

That  is,  the  net  sum  of  the  receipts  at  home  (of  money,  bank 
credit,  and  book  credit)  plus  the  sum  of  pa3Tnents  for  goods 
coming  inward,  is  equal  to  the  sum  of  the  value  of  the  goods 
sold  at  home  plus  the  value  of  those  sent  out  of  the  country. 
The  last  two  equations,  one  relating  to  purchases  and  the 
other  to  sales,  may  be  added  together  so  as  to  give  in  a  com- 
mon equation  the  total  trade  in  which  the  given  community 
is  concerned,  that  is,  the  total  sales  and  purchases  within 
itself  and  the  sales  and  purchases  with  respect  to  the  outside 
world.     The  combined  equation  will  be:  — 

2  2jy  +  20  +  27  =  2  ^pnQn  +  ^PiQi  +  SpoQo. 

Here  the  internal  trade  is  counted  twice,  because  every  trans- 
action occurs  both  as  a  sale  and  as  a  purchase.     This  expresses 


374        THE   PURCHASING   POWER  OF  MONEY      [Append.  VI 

the  equation  of  exchange  for  the  total  trade  (domestic  and 
foreign)  in  which  the  country  under  consideration  engages. 
If,  instead  of  adding,  we  subtract  one  equation  from  the 
other,  we  obtain  the  following :  — 

20  -  27  =  %ViQi  -  2poQo 

which  is  the  equation  of  the  balance  of  trade  in  its  most 
general  form,  taking  account,  as  it  does,  of  credit  as  well  as 
of  money.  The  flow  of  money,  as  to  or  from  a  nation,  depends 
upon  this  last  equation. 

The  right-hand  side  of  the  penultimate  equation,  depends 
on  three  sets  of  prices, — the  home  prices  (the  p^'s),  the  prices 
of  goods  which  come  into  the  country  (the  p/s),  and  the 
prices  of  goods  which  go  out  (the  po's) . 

If,  for  instance,  thep/,'s  are  extremely  high,  the  consequence 
will  be  a  stimulus  to  goods  coming  in  (Qj)  and  a  discouragement 
to  goods  going  out  (Qo),  thus  tending  to  make  the  right  side  of 
the  last  equation  large  and,  therefore,  also  increasing  the  left 
side.  In  other  words,  there  will  be  a  so-called  unfavorable 
balance  of  trade  and  a  tendency  for  media  of  payments  to  go 
out  rather  than  to  come  in;  that  is,  there  will  be  an  outflow  of 
money  (indicated  by  0) ,  or  a  transfer  of  bank  credit  to  foreigners 
(0'),  or  a  charging  on  the  books  of  the  foreigners  (0")>  or  a  less- 
ening of  the  liquidations  of  previous  book  accounts  {0'")  ;  or 
else  there  will  be  opposite  changes  in  7,  I',  I",  7'";  or  finally, 
a  combination  of  both  tendencies,  while  temporarily  there 
will  be  fluctuations  between  these  various  magnitudes.  In 
the  long  run  and  in  the  last  analysis,  the  changes  will  relate 
largely  to  the  actual  export  and  import  of  money,  that  is, 
will  concern  the  unprimed  magnitudes  0  and  7. 

For  a  large  country  like  the  United  States,  the  outside 
trade  is  so  small,  compared  with  the  internal  trade,  as  to  be 
negligible.  As  we  shall  see  in  Chapter  XII,  the  foreign 
trade  of  the  United  States  is  only  a  fraction  of  one  per  cent 
of  the  internal  trade.  And,  because  the  export  and  import 
sides  of  the  various  magnitudes   (O's,   7's,   Qo's  and  Q<'s) 


Sec.  1]  APPENDIX  TO   CHAPTER   VI  375 

nearly  cancel  each  other,  the  net  balance  remaming  on  either 
side  of  the  equation  of  exchange  seldom  amounts  to  more 
than  one  eighth  of  one  per  cent  of  the  internal  trade  of  the 
United  States. 

Almost  equally  insignificant  is  the  difference,  E"  —  E'", 
between  debts  annually  contracted  and  liquidated,  if  we  may 
judge  from  estimates  of  that  indebtedness,  such  as  Hohnes's. 
We  are  at  any  rate  safe  in  saying  that  the  corrections  to  our 
equation  of  exchange  which  have  been  discussed  in  this  and 
the  previous  section  are  needless  complications  so  far  as  the 
United  States  is  concerned.  We  may  therefore  consider  the 
equation  MV  +  M'V  =  2pQ  as  practically  a  precise  form  of 
the  equation. 


APPENDIX  TO  CHAPTER  VII 

§  1  (to  Chapter  VII,  §  2) 

Money  Substitutes  Unlike  Other  Substitutes 

Much  reasoning  has  been  based  upon  the  assumption  that 
the  price  determination  of  two  commodities  used  as  money 
is  analogous  to  that  of  any  other  two  commodities.  It  is 
clear,  however,  that  two  forms  of  money  differ  from  a  random 
pair  of  commodities  in  being  substitutes.^  Two  substitutes 
proper  are  regarded  by  the  consumer  as  a  single  commodity. 
This  lumping  together  of  the  two  commodities  reduces  the 
number  of  demand  conditions,  but  does  not  introduce  any 
indeterminateness  into  the  problem  because  the  missing 
conditions  are  at  once  supplied  by  a  fixed  ratio  of  substitution. 
Thus,  if  ten  pounds  of  cane  sugar  serve  the  same  purpose  as 
eleven  pounds  of  beet-root  sugar,  their  fixed  ratio  of  substitu- 
tion is  ten  to  eleven ;  or  if  a  bushel  of  India  wheat  can  replace 
a  bushel  of  Dakota  wheat,  the  substitution  ratio  is  unity. 
In  these  cases,  the  fixed  ratio  is  based  on  the  relative  capaci- 
ties of  the  two  commodities  to  fill  a  common  need,  and  is 
quite  antecedent  to  their  prices.  Ten  pounds  of  cane  sugar 
can  replace  eleven  pounds  of  beet-root  sugar  so  long  as  human 
taste  marks  no  other  ratio.  India  and  Dakota  wheat  have 
the  same  desirability  or  utility  because  they  have  the  same 
relation  to  man's  tastes.     No  change  of  market  conditions, 

^  Substitutes  merely  in  the  sense  of  Gresham's  Law  that  the 
cheaper  will  be  substituted  for  the  dearer.  It  does  not  deny  that 
the  metals  are  differently  preferred  for  different  monetary  uses. 
We  cannot  compare  gold  and  silver  to  independent  commodities  as 
"copper  and  wheat,"  or  "beef  and  shoes,"  but  only  to  some  other 
pair  of  substitutes,  or  quasi  substitutes,  such  as  iron  and  steel, 
cotton  and  wool,  oats  and  maize,  molasses  and  sorghum,  cane  and 
beet-root  sugar,  India  and  Dakota  wheat. 

376 


Sec.  1]  APPENDIX  TO   CHAPTER  VII  377 

no  change  of  price,  could  make  a  consumer  regard  one  bushel 
of  India  wheat  as  equivalent  to  two  of  Dakota.  The  sub- 
stitution ratio  is  fixed  by  nature,  and  in  turn  fixes  the  price 
ratio. 

In  the  single  case  of  money,  however,  there  is  no  fixed 
ratio  of  substitution.  In  one  age,  ten  ounces  of  silver  may 
circulate  as  the  equivalent  of  one  of  gold ;  in  another,  twenty 
ounces.  No  human  taste  or  need  will  interfere.  We  have 
here  to  deal,  not  with  relative  sweetening  power,  nor  relative 
nourishing  power,  nor  with  any  other  capacity  to  satisfy 
wants  —  no  capacity  inherent  in  the  metals  and  independent 
of  their  prices.  We  have  instead  to  deal  only  with  relative 
purchasing  power.  We  do  not  reckon  a  utihty  in  the  metal 
itself,  but  in  the  commodities  it  will  buy.  We  assign  their 
respective  desirabilities  or  utilities  to  the  sugars  or  the  wheats 
before  we  know  their  prices,  but  we  must  first  inquire  the 
relative  circulating  value  of  gold  and  silver  before  we  can 
know  at  what  ratio  we  ourselves  prize  them.  To  us  the  ratio 
of  substitution  is  identically  the  price  ratio  and  therefore  can 
have  no  influence  in  fixing  that  ratio.  The  case  of  two  forms 
of  money  is  unique.  They  are  substitutes,  but  have  no  natural 
ratio  of  substitution,  dependent  on  consumers'  preferences. 

The  foregoing  considerations  are  emphasized  for  the  reason 
that  they  are  overlooked  by  those  writers  who  imagine  that  a 
fixed  legal  ratio  is  merely  superimposed  upon  a  system  of 
supply  and  demand  already  determinate,  and  who  seek  to 
prove  thereby  that  such  a  ratio  is  foredoomed  to  failure.  This 
is  the  monometallist's  favorite  analogy.  It  is  unsound, 
though  its  unsoundness  does  not  necessarily  involve  the  un- 
soundness of  the  monometalhst's  general  conclusions.  Gold 
and  silver  or  any  other  two  commodities  which  serve  the 
purposes  of  money  are  not  analogous  to  two  ordinary  and 
unrelated  articles  and  are  not  completely  analogous  even  to 
two  substitutes,  because,  for  two  forms  of  money,  there  is  no 
consumer's  natural  ratio  of  substitution.  There  seems, 
therefore,  room  for  an  artificial  ratio.  We  shall  see,  however, 
that  there  are  limits  beyond  which  an  artificial  ratio  will  fail. 


378       THE   PURCHASING   POWER  OF  MONEY      [Append.  VII 

§  2  (to  Chapter  VII,  §  2) 

Limits  for  Ratios  within  which  Bimetallism  is  Possible 

A  change  of  ratio  is  represented  by  a  reconstruction  of  our 
reservoirs  in  new  units,  but  we  can,  without  the  trouble 
of  such  a  transformation,  exhibit  on  the  mechanism  as  it 
stands  the  limiting  ratios  between  which  bimetallism  is  pos- 
sible. Suppose  the  film  in  Figure  76  to  be  forced,  firstly  to 
its  extreme  right  limit,  and  secondly  to  its  extreme  left,  and 
in  each  case  permanent  equilibrium  to  be  attained.  In  the 
one  case  there  is  a  premium  on  gold,  in  the  other,  a  premium 
on  silver.  These  premiums  mark  the  divergences  from  the 
given  ratio  which  are  possible  without  destroying  bimetallism. 
Thus  suppose  the  legal  ratio  and  that  for  which  the  mecha- 
nism is  constructed  is  32  of  silver  to  1  of  gold  and  that,  when 
the  film  is  moved  to  the  left  limit,  the  level  of  gold  will  be  be- 
low 00  a  distance  ^  as  great  as  the  silver  level,  while  at  the 
right  limit  it  will  be  |.  Then  the  ratio  32  to  1  can  be  varied 
between  the  factors  |  of  32  to  1  and  f  of  32  to  1  and  bimetal- 
lism would  succeed  at  any  ratio  between  32  X  i  to  1  and 
32  X  I  to  1,  i.e.  between  28  to  1  and  40  to  1.  A  ratio  below 
28  to  1,  such  as  the  famous  16  to  1,  would  ultimately  convert 
gold  monometallism  into  silver  monometallism,  but  would 
be  inoperative  in  the  opposite  direction.  A  ratio  above  40 
to  1,  such  as  50  to  1,  would  ultimately  convert  silver  mono- 
metallism into  gold  monometalUsm.  A  ratio  between  the 
two  extremes  would  result  in  neither  sort  of  monometallism 
but  in  bimetallism.  The  statistical  determination  of  these 
limits  is,  of  course,  a  problem  which  cannot  with  present 
knowledge  be  solved.  The  figures  28  and  40  are  not  intended 
as  guesses,  but  purely  as  illustrations. 


APPENDIX  TO  CHAPTER  VIII 

§  1  (to  Chapter  VIII,  §  6) 

Statistics  of  Turnover  at  Yale  University 

The  rate  of  turnover  of  money  varies  with  the  amount  of 
money  expended  at  a  given  level  of  prices.  In  other  words,  it 
varies  with  the  volume  of  trade  of  the  individual.  The  statis- 
tics of  turnover  among  Yale  students  form  two  series,  the 
first  or  earlier  showing  an  average  velocity  or  rate  of  turn- 
over of  34  per  year,  the  second  or  later,  of  66.  The  differ- 
ence is  probably  due  in  part  to  the  higher  expenditure  of  the 
second  group  of  students,  although  it  is  probably  chiefly  ac- 
counted for  by  the  fact  that  the  first  series  were  not  ac- 
curate. Each  student  in  the  first  series  was  simply  asked 
to  estimate  roughly  his  annual  cash  expenditure  and  the 
average  cash  on  hand.  The  quotient  of  the  first  divided  by 
the  second  showed  his  rate  of  turnover.  Estimates  were 
received  from  128  men.  The  average  annual  expenditure  in 
cash  was  $514  and  the  average  cash  on  hand,  $15,  yielding 
the  quotient  34  times  a  year  as  the  average  rate  of  turnover. 
These  estimates,  being  usually  little  more  than  guesses,  may 
have  been  wide  of  the  mark.  In  order  to  obtain  a  more 
exact  estimate  the  second  series  was  undertaken.  The  plan 
was  adopted  of  asking  volunteers  to  keep  an  exact  account 
for  one  month  of  the  daily  cash  expenditures  and  balances 
at  the  beginning  and  end  of  each  day.  It  was  found  from 
these  statistics  that  for  the  113  individuals  who  contributed 
these  new  data,  the  average  annual  rate  of  expenditure  was 
$660  and  an  average  cash  on  hand  was  almost  exactly  $10, 
giving  the  quotient  66  times  a  year.  The  rougher  estimates, 
the  average  of  which  was  34,  have  so  little  weight  compared 
with  the  accurate  records,  the  average  of  which  was  66,  that 
we  may  place  the  general  average  at  60,  the  nearest  round 
number  below  66.     Besides  the  two  student  series,  returns 

379 


380      THE    PURCHASING  POWER   OF  MONEY     [Append.  VIII 


were  received  from  five  other  persons.  One  was  a  stenogra- 
pher who,  during  a  month,  spent  at  the  rate  of  $435  a  year 
and  had  an  average  cash  balance  of  $7.86,  making  her  turn- 
over rate  55  times  a  year.  Another  was  a  young  hbrarian 
whose  cash  expenditures,  kept  carefully  for  six  months, 
showed  a  rate  of  $854  a  year  and  whose  average  cash  bal- 
ance was  $10.41,  making  a  rate  of  82  times  a  year.  A  third 
was  a  lawyer  who  made  a  practice  of  paying  all  bills  in  cash, 
and  as  these  amounted  to  some  $4000  a  year,  he  carried  in  his 
pocket  an  average  cash  balance  estimated  at  $175,  This 
figure  he  regarded  as  correct  within  $15.  His  velocity  of 
circulation,  on  the  basis  of  4000  divided  by  175,  shows  23 
times  a  year.  The  other  two  cases  were  of  professors.  The 
first,  from  careful  records,  found  that  he  turned  over  his  cash 
37  times  a  year  and  turned  over  his  bank  account  52  times  a 
year.  The  second  roughly  estimated  his  rjite  of  cash  turnover 
at  175  and  of  bank  deposits  at  25. 

Of  the  total  2  46  persons  whose  records  were  collected,  only 
116  had  kept  careful  accounts.  Of  these  116,  all  except  three 
were  students.  The  reason  for  believing  that  the  lower  veloc- 
ity of  the  first  series  is  not  wholly  accounted  for  by  its  being 
erroneously  estimated,  but  is  partly  due  to  the  smaller  ex- 
penditures of  that  group,  is  based  on  the  fact  that  we  find  a 
distinct  relation  between  amount  of  expenditure  and  rate  of 
turnover  within  each  group.  Thus,  if  we  separate  the  113 
students  who  gave  careful  returns  into  two  groups,  one, 
those  who  spend  less  than  $50  a  month  and  the  other  those 
who  spend  $50  and  over,  we  find  the  following  figures  :  — 


Expending  less  than  $600  a 
year 

Expending  $600  and  over  a 
year 


No.  OF 

Cases 


72 
41 


Average 
Annual 
Rate  of 
Expendi- 
ture 


i  367 
1175 


Average 

Cash 
Balance 


5  8.60 
12.70 


Vel.  op 
Circu- 
lation 


43 
93 


Sec.  1] 


APPENDIX   TO   CHAPTER   VIII 


381 


Here  we  see  that  the  richer  men  averaged  about  three  times 
as  great  an  expenditure  as  the  poorer,  but  carried  only  50 
per  cent  more  cash  on  hand.  In  consequence,  the  velocity 
of  the  richer  was  93  as  against  43  for  the  poorer,  or  more  than 
double.  The  progressive  relation  between  expenditure  and 
rate  of  turnover  may  be  seen  by  arranging  the  113  cases  into 
five  groups  according  to  expenditure. 


No.  OF 

Cases 


Average 
Expendi- 
ture 


Vel.  of 
Circu- 
lation 


Expending  less  than  $300  a  year 
Expending  over  $300  and  under 

a  year     

Expending  over  $600  and  under  $900 

a  year 

Expending  over  $900  and  under  $1200 

a  year     

Expending  over  $1200  a  year    .     .     . 


22 
50 
19 

10 

12 


179 
450 

781 

1012 
1936 


17 

59 

61 

96 
137 


The  number  of  cases  is  small,  but  the  results  are  uniformly 
consistent.  They  show  that  velocity  and  expenditure  are 
directly  correlated.  Even  the  other  series  (of  rough  esti- 
mates) show  the  same  general  relation.  Taking  the  same 
classifications  for  expenditure,  we  find  that  the  velocities  are 
22,  30,  44,  88,  32.  Here  the  only  exception  is  the  last  figure, 
which,  as  it  is  the  average  of  only  five  individuals,  is  an  ex- 
ception of  httle  importance.  We  conclude,  therefore,  with 
at  least  a  moderate  degree  of  confidence,  that  for  a  given 
price  level,  the  greater  the  expenditure  the  higher  the  rate  of 
turnover.  In  other  words,  persons  who  spend  money  faster 
absolutely  than  others  also  spend  it  faster  relatively  to  the 
amount  kept  on  hand.  The  amount  kept  on  hand  by  the 
rich,  though  larger  absolutely  than  that  kept  on  hand  by 
the  poor,  is  smaller  relatively  to  the  expenditure. 

This  law  of  increasing  velocity  with  increasing  expenditure 
agrees  with  the  general  fact  that  the  larger  the  scale  of  any 
business  operation,  the  greater  the  economy.  Small  stores 
have  to  keep  a  larger  stock  relatively  to  their  business  than 


382      THE   PURCHASING  POWER  OF  MONEY     [Append.  VIII 

larger  stores.  Likewise,  small  banks  have  to  keep  a  larger 
reserve  in  proportion  to  business  transacted.  Professor 
Edgeworth  has  shown  a  mathematical  basis  for  the  fact  that 
the  larger  the  bank,  the  smaller  relatively  the  reserve  needed. 
Hence,  we  need  not  be  surprised  to  find  that  the  small  pur- 
chaser finds  it  well  to  keep  on  hand  a  relatively  larger  stock 
of  money  than  the  large  purchaser. 

The  data  are  too  meager  to  state  any  exact  quantitative 
relation  between  velocity  and  expenditure.  They  show  that 
velocity  increases  as  expenditure  increases.  But  beyond 
this  we  cannot  safely  go.  The  data  seem  to  point  to  the 
conclusion,  however,  that  the  velocity  increases  in  a  smaller 
ratio  than  expenditure. 

§  2  (to  Chapter  VIII,  §  8) 

Four  Types  of  Commodities  Contrasted 

Let  us  assume  four  sorts  of  commodities  which  we  may, 
for  convenience,  designate  as  wine,  sugar,  beef,  and  salt. 
We  shall  suppose  that  a  reduction  in  the  respective  prices 
of  these  will  have  in  each  case  a  different  effect  on  the  sale. 
Accordingly  we  shall  witness  four  possible  effects  on  the 
general  price  level,  following  a  reduction  in  the  price  of  the 
four  commodities  respectively. 

First,  wine.  This  is  assumed  to  be  a  commodity  of  such  a 
sort  that  a  reduction  in  its  price  will  be  accompanied  by  a 
more  than  proportionate  increase  in  its  sale.  Thus  the  total 
amount  of  money  expended  for  wine  will  be  increased.  This 
leaves  a  less  amount  with  which  to  buy  other  commodities. 
In  consequence,  the  prices  of  these  other  commodities,  as  well 
as  of  the  wine  itself,  must  fall. 

Next,  as  to  sugar.  This  is  assumed  to  be  such  a  commodity 
that  a  reduction  in  its  price  will  be  accompanied  by  an 
exactly  proportionate  increase  in  sales ;  so  that  the  total 
money  expended  upon  sugar  will  be  unchanged.  Under  these 
circumstances  the  amount  of  money  to  be  expended  in  ex- 


Sec.  2]  APPENDIX  TO   CHAPTER  VIII  383 

change  for  other  things  will  be  neither  increased  nor  de- 
creased, and  other  prices  will  remain  unchanged ;  but  the 
general  level  of  prices,  including  that  of  sugar  itself,  will  be 
slightly  lowered  because  the  fall  of  one  commodity,  when 
others  do  not  change,  must  produce  some  decrease  in  the 
average. 

Third,  as  to  beef.  This  typifies  what  is  called  a  "neces- 
sary." We  assume  that  a  reduction  in  its  price  will  be  ac- 
companied by  an  increase  in  consumption,  but  not  sufficient 
to  absorb  all  the  money  that  was  previously  spent  for  it. 
The  total  expenditure  for  beef  will  thus  be  reduced,  and  in 
consequence  there  will  be  set  free  a  certain  amount  of  money 
to  be  expended  for  other  goods,  the  prices  of  which  will, 
therefore,  in  general,  rise  slightly.  The  net  effect,  however, 
will  be  an  infinitesimal  fall  of  general  prices,  including  beef ; 
for  to  the  slight  extent  that  there  has  been  an  increase  of 
the  total  of  goods  sold  by  reason  of  the  increase  in  the  sales 
of  beef,  without  any  increase  in  the  total  amount  of  money  spent, 
there  must  be  a  fall  in  the  average  prices.^ 

Lastly,  as  to  salt.  This  is  assumed  to  be  an  "absolute 
necessary,"  so  that  a  reduction  in  its  price  will  not  affect  the 
amount  sold.  The  result  will  be  that  the  general  price  level 
will  be  unaffected,  the  fall  in  the  price  of  salt  being  exactly 
offset  by  a  compensatory  rise  in  other  prices,  and  the  total 
volume  of  trade  remaining  unchanged. 

We  see  then  that  the  degree  of  fall  in  price  level  due  to 
the  fall  in  a  single  price  may  be  great  or  small  or  nothing  at 
all,  according  to  circumstances. 

In  all  of  the  four  foregoing  illustrations,  it  was  assumed 
that  the  fall  in  the  individual  price  originated  in  a  change  in 
the  supply  curve  or  schedule.     If  the  fall  in  price  originates 

^  The  mathematical  necessity  of  this  result  can  be  seen  from  the 
formulae  in  the  Appendix  to  Chapter  X,  where  the  right  side  of  the 
equation  of  exchange  is  transformed  into  the  product  of  two  factors, 
the  volume  of  trade  (T)  and  the  price  level  (P).  If  their  product 
remains  the  same,  an  increase  in  the  volume  of  trade,  however  small, 
must  cause  a  decrease  in  the  price  level. 


384      THE   PURCHASING   POWER   OF  MONEY     [Append.  VIII 

in  a  change  in  the  demand  curve  or  schedule,  there  will  in 
general  be  a  rise  in  other  prices  and  in  the  general  price 
level,  for,  there  being  less  of  the  particular  commodity  bought 
and  that  at  a  less  price,  there  will  be  less  spent  upon  it  and 
therefore  more  on  other  commodities,  the  price  of  which  will 
be  higher  and,  as  the  reduction  in  the  amount  bought  of  the 
particular  commodity  will,  in  general,  imply  a  reduction  in 
the  total  volume  of  trade,  the  general  price  level  will  be 
raised.^ 

^See  Irving  Fisher,  "Mathematical  Investigations  in  the  Theory 
of  Value  and  Prices,"  Transactions  of  the  Connecticut  Academy  of 
Arts  and  Sciences,  1892,  p.  51. 


APPENDIX  TO  CHAPTER  X 

§  1.  Each  Form  of  Index  Number  for  Prices  implies  a  Cor- 
relative Form  of  Index  Number  for  Quantities 

We  have  seen  that  the  number  of  possible  forms  of  aver- 
ages is  infinite.  Since  an  index  number,  as  Pi,  is  an  average, 
it  follows  that  there  exists  an  infinite  number  of  possible 
forms  of  index  numbers.  Forty-four  of  the  simplest  and 
most  important  forms  are  given  in  the  table  which  follows. 
In  this  table  the  subscript  "  i  "  relates  to  any  specified  year 
called  for  convenience  "year  1,"  while  the  subscript  "0" 
likewise  relates  to  "  year  0,"  called  the  "  base  "  year.  The 
headings  of  the  columns  in  the  table  give  the  formula  for 
the  index  number.  Pi,  for  the  year  1  relatively  to  the  base 
year  0.  By  substituting  "2"  for  "  1,"  each  formula  could 
be  made  to  refer  to  a  second  year,  2,  considered  relatively  to 
the  base  year  0.  Likewise,  substituting  "  3,"  "4,"  etc.,  for 
"  1,"  we  have  an  entire  series  of  index  numbers.  Pi,  P2,  P3, 
P4,  etc.,  for  different  years,  all  relative  to  the  same  base  year 
0.  Since  the  formulae  are  all  aUke  and  differ  only  in  sub- 
scripts, it  is  unnecessary  to  waste  space  by  expressing  P2, 
P3,  etc.,  in  the  headings.  Consequently,  in  each  column 
heading,  only  the  formula  for  Pi  is  expressed. 

Also  to  save  space,  the  column  headings  omit  the  formulae 
for  Ti,  etc.,  correlative  to  those  for  Pi.  Each  form  of  price 
index,  Pi,  applicable  to  the  equation  of  exchange,  implies  a 
correlative  trade  index,  Ti,  such  that  the  product  of  the  two 
is  equal  to  SpiQi,  the  right  side  of  the  equation  of  exchange. 

Since  PiT^i  =  %piQi, 

it  foUows  that  Ti  =  ?^^ 
Pi 

Hence,  given  a  particular  formula  for  Pi,  we  have  a  result- 
ant and  particular  formula  for  Ti.     For  instance,  if  Pi  is  a 
2  c  385 


386  THE   PURCHASING   POWER  OF  MONEY      [Append.  X 


,(re) 


simple   arithmetic  average  of    ^,  ^,  ^-r^,  •••  ~^,    i.e.   if 

Po    Po    p   0         p^  ^0 

1  'n 

Pi  =  -  2—  (formula  3  of  the  table),  where  n  is  the  num- 
n     po 

ber  of  commodities  of  which  the  price  ratios  are  included, 

then  the  correlative  formula  for  Ti  will  evidently  be 

rp  _  SpiQi  _  SpiQi 

*         Pi         1  2Pi" 

n     po 

Again,  if  Pi  is  the  geometric  average  \/—  *  ^  "  ^-rr  '"  ^-r^ 

^Po    Po    p  0       p%i 

(formula  7  of  the  table),  then  Ti  has  the  correlative  form 


"/pTTpT 

^Po    p'o 


Conversely  any  particular  formula  for  Ti  implies  a  correl- 
ative particular  formula  for  Pi.     For,  since 

PiTi  =  SpiQi, 
it  follows  that  p  _  SpiQi 

By  means  of  this  equation,  if  we  have  given  any  particu- 
lar formula  for  Ti,  we  may  obtain  a  resultant  particular 
formula  for  Pi. 

The  examples  already  given  of  Pi  (the  arithmetical  and  geo- 
metric average)  illustrate  how  to  obtain  the  correlative  formula 
for  Ti.  If  we  work  backward  from  these  somewhat  compli- 
cated formulae  for  Ti,  we  may  in  turn  derive  as  the  correla- 
tive formulae  for  Pi  the  arithmetic  and  geometric  averages. 

As  a  third  example  illustrating  the  derivation  of  the 
formula  for  Pi  from  a  given  formula  for  Ti,  let  Ti  be 
defined  as  SpoQi,"  then 

'        Ti       SpoQi' 
(Formula  11  of  the  table.) 


Sec.  11  APPENDIX   TO   CHAPTER   X  387 

We  may  consider,  then,  that  each  column  heading,  though 
stating  only  the  formula  for  Pi,  implies  also  a  corresponding 
formula  for  Ti ;  that  is,  Pi  and  Ti  occur  in  correlative  pairs. 
Pi  and  Ti  are  such  that  if  one  of  them  (say  Pi)  is  given 
independently  of  the  equation,  SpiQi  =  PiTi,  the  other  is 
then  defined  by  means  of  that  equation. 

The  two  magnitudes  Pi  and  Ti  are  not,  however,  abso- 
lutely symmetrical.  There  is  this  important  distinction 
between  them:  that,  while  Pi  is  an  abstract  number,  Ti  is 
concrete,  being  expressible  in  dollars  and  cents. 

It  thus  appears  that,  although  the  p's  and  Q's  enter  sym- 
metrically into  the  expression  SpiQi,  yet,  when  this  expression 
is  replaced  by  PiTi,  the  first  factor,  Pi,  represents  the  p's  in 
a  somewhat  different  manner  from  that  in  which  the  second 
factor,  Ti,  represents  the  Q's.  Pi  is  a  pure  number,  an  aver- 
age of  pure  numbers  —  the  ratios  the  p's  bear  to  the  base 

prices,  po's,  whereas  Ti,  being  -^~'  is  a  concrete  number, 

Pi 

being  a  value  found  by  dividing  the  value  ^piQi  by  the 
pure  number  Pi. 

Thus,  while  the  p's  and  Q's  occur  symmetrically  in  the 
original  formula  2piQi,  the  process  by  which  we  convert 
2piQi  into  PiTi  treats  them  asymmetrically.  But  evidently 
we  can  reverse  the  asymmetry  in  their  treatment;  for,  in- 
stead of  putting  SpiQi  equal  to  PiTi,  we  may  put  it  equal  to 
AiQi,  in  which  ^i  is  now  a  quantity  index,  that  is,  an  average 
of  the  ratios  which  the  Qi's  bear  to  the  Qo's  or  base  quanti- 
ties (i.e.  an  average  of  ^^  •  Mr  *  ^77  •"  ),  and  Ai,  being 
\  Qo    Q  0    Q  0     J 

therefore  -£^,  is  the  "aggregate  price,"  that  is,  the  value 

found  by  dividing  the  value  SpiQi  by  the  pure  number  Qi. 
Here,  if  the  form  of  Qi  is  given  independently  of  the  equa- 
tion SpiQi  =  ^4.1^,  the  form  of  Ai  is  defined  by  means  of  this 
equation,  and  conversely. 

Thus  we  may  convert  SpiQi  into  either  PiTi  or  AiQi.  In 
the  first,  the  p's  are  represented  by  a  ratio.  Pi ;  in  the  second, 


388  THE   PURCHASING   POWER  OF  MONEY      [Append.  X 

by  a  value,  Ai;  in  the  first,  the  Q's  are  represented  by  a  value, 
Ti ;  in  the  second,  by  a  ratio,  ^i.  The  asymmetry  of  each  of 
the  two  formulae  PiTi  and  AiQi  is  the  reverse  of  the  other. 

Finally  we  may,  if  we  wish,  treat  both  the  p's  and  Q's 
alike  by  putting  SpiQi  equal  to  ('^poQo)PiQi,  where  Pi  and  Qi 
are,  both  of  them,  index  numbers  for  the  pi's  and  Qi's 
respectively.    That  is  (as  we  shall  prove).  Pi  and   ^i  are 

averages  respectively  of  price  ratios  like  ^'  and  of  quantity 

Po 

ratios  like  ^-     The  equation  ^piQi=  {^poQo)PiQi  may  be 

said  to  define  either  one  of  the  two  averages  (Pi  and  ^i)  in 
terms  of  the  other.  One  or  the  other  must  be  defined  irre- 
spective of  the  equation. 

Thus  there  are  three  ways  of  resolving  ^piQi,  as  follows  : — • 

MQi  =  PiTi  =  AiQi  =  (2poQo)Pi(?i. 

The  third  form  becomes,  dividing  the  equation  through  by 
^PoQo, 

We  wish  now  to  prove  that  if  either  Pi  or  Qi  is  first  de- 
termined in  any  way  conformably  to  the  definition  of  an 
average,  leaving  the  other  to  be  determined  by  the  above 
equation,  then  the  latter  also  necessarily  conforms  to  the 
definition  of  an  average.     We  have  to  prove  that  if  Qi  is 

O      O' 
taken  as  an  average  of  ^,   xr"*'  ^^^n  the  correlative  ex- 

pression  for  Pi  derived  from  (1),  viz.:  — 

is  an  average  of  ^,^'".   It  is,  therefore,  only  necessary  to 
Po  p  0 

show  (in  accordance  with  the  most  general  definition  of  an 


Sec.  11  APPENDIX  TO   CHAPTER  X  389 

average  as  given  in  the  Appendix  to  Chapter  II)  that  ex- 
pression (2)  shall  be  equal  to  k  when 

Po     p'o 
(and  when  at  the  same  time 

Qo    Q'o  / 

We  therefore  suppose  that 

Pl-P'i  = J. 

—  —J.  —  Kf 

Po     Po 
so  that  pi  =  kpo ;  p\  =  kp'o',  ••• ; 

and  also  that  ^  =  ir  =  -  =  ^'» 

Qo     Q  0 

so  that  Qi  =  k'Qo;  Q\  =  k'Q\;  -. 

Then  SpiQi  =  2(fcpo  X  k'Q^)  =  kk'  ^poQo. 

Now,  since  ^^^=""^^'» 

it  follows  that    (av.  ^,  ^,..-)  =  k' 
\         Qo    Q  0       / 

by  the  definition  of  an  average. 

Hence  the  expression  (2)  may  now  be  written 

kk'  SpoQo 

which  is  evidently  equal  to  k. 

Therefore  expression  (2)  is,  by  definition,  an  average  of 

2l,  2j...^    By  the  same  reasoning  we  may  show  conversely 
Po    Po 

2poQo 


that 


fAv.  21,  HJ...^ 

V  Po     Po      J 


is  a  true  average  of  ^S  ^•••-    We  conclude  that  if  either 


390         THE  PURCHASING  POWER  OF  MONET     [Append.  X 

Pi  or  Oi  in  the  formula  PiQi  =  -z^—  is  an  average  of  the  p  or 

SpoQo 

Q  ratios  respectively,  then  the  other  is  also  an  average  re- 
spectively of  the  Q  or  p  ratios. 

§  2.  Index  Numbers  for  Prices  occur  in  Antithetical  Pairs  as 
also  do  Index  Numbers  for  Quantities 

We  have  seen  that,  given  any  special  form  of  average  for 
Pi,  there  results  therefrom  a  correlative  form  for  ^i  and  vice 

versa.    Thus  if  Pi  is  the  simple  arithmetical  average  -  2^> 

n    po 
SpiQi 

then  Q\  is  .    Again,  if  we  start  with  Qi  as  the  simple 

n    po 

arithmetical  average  -  2  ^  then  we  discover  in  its  correlate 
n    Qo 

SpiQi 

a  new  formula  for  Pi,  viz.  °.    In  this  way  any  given 

n  Qo 
formula  for  Pi  leads  to  another  formula  for  Pi  which  may  be 
called  its  antithesis.  This  second  formula  for  Pi  is  identical 
in  form  with  the  formula  for  ^i  correlative  to  the  first  for- 
mula for  Pi,  dififering  merely  in  the  fact  that  the  pi's  and  Qi's 
are  interchanged. 

The  four  forms  and  their  relations  are  best  seen  by  placing 
them  in  a  square,  as  in  the  following  example  :  — 

221  SpiQi 

Pi  =  -^  antithetical  to  Pi  =  ^^ 

correlative  to  correlative  to 

SpiQi  ^Qi 

^1  =  ^  antithetical  to  Pi  =  -^- 

l^Pi  n 

n   Po 


Sec.  2]  APPENDIX  TO   CHAPTER  X  391 

The  pair  of  formulae  in  the  left  vertical  column  express 
correlative  formulae,  one  for  Pi  and  the  other  for  Qi.  The 
formula  diagonally  opposite  each  of  these  has  the  p's  and 
Q's  interchanged.  The  right  pair  thus  formed  are  evidently 
also  correlates  of  each  other  and  each  is  the  antithesis  of  that 
in  the  same  horizontal  line  at  its  left.  Since  any  formula 
for  Pi  involves  an  antithetical  formula  for  Pi,  we  have  here 
a  means  of  devising  new  formulae  from  old  and  also  of  noting 
certain  unsuspected  relationships  between  formulae  already 
in  use. 

In  the  table  of  index  numbers  for  Pi  which  follows,  the 
antithetical  formulae  are  in  each  case  placed  side  by  side 
and  joined  by  a  bracket.  The  two  together  represent,  in 
each  case,  the  upper  half  of  a  square  like  the  above.  The 
omitted  lower  half,  giving  the  correlative  forms  for  ^i,  can 
be  readily  suppUed  in  every  case;  but,  to  save  space,  each 
column  heading  in  the  table  only  includes  the  formula  for 
Pi,  omitting  its  correlate  for  ^i  as  well  as  the  corresponding 
formulae  for  Ti  and  Ai.  The  formula  for  ^i  is,  as  above 
explained,  easily  written  by  interchanging  p's  and  Q's  in  the 
formula  given  in  the  neighboring  (antithetical)  columns; 
that  for  Ti  is  found  by  dividing  SpiQi  by  Pi;  that  for  Ai  by 
dividing  SpiQi  by  ^i.  Practically  Pi  and  Ai  serve  the  same 
purpose,  namely,  that  of  indicating  price  changes;  likewise 
Qi  and  Ti  serve  the  same  purpose,  namely,  that  of  indicating 
quantity  changes.  For  any  series  of  years  the  numbers  for 
Pi  and  for  Ai  will  be  proportional,  the  only  difference  being 
that  Pi  is  expressed  in  percentages,  the  figure  for  the  base  year 
being  100  per  cent,  whereas  Ai  is  expressed  in  dollars,  the  fig- 
ure for  the  base  year  being  the  actual  exchanges  2poQo  in 
that  year.  Likewise  Qi  and  Ti  differ  merely  as  percentage 
and  dollar  measurements,  the  base  figure  being  100  per  cent 
and  SpoQo  dollars  respectively. 


d92         THE   PURCHASING   POWER  OF  MONEY      [Append.  X 

§  3.   General  Meanings  of  p's  and  Q's 

We  may  here  pause  to  point  out  that  the  whole  present 
discussion  relates  purely  to  the  form  of  an  index  number  of 
p's  and  Q's  without  reference  to  the  meaning  to  be  assigned 
to  these  p's  and  Q's.  These  meanings  may  be  far  wider 
than  simply  the  prices  and  quantities  in  the  equation  of 
exchange.  For  example,  an  index  number  of  prices  may  be 
constructed  with  reference  to  the  purchasing  power  of  a 
workman's  wages.  In  this  case,  the  same  formula  as  be- 
fore, 2piQi,  may  be  employed,  but  the  terms  have  different 
meanings.  The  p's  now  relate  to  the  prices  of  goods  enter- 
ing into  the  workmen's  budgets,  and  the  Q's  to  the  quantities 
of  workmen's  goods  entering  into  their  consumption.  In  this 
case,  the  price  index,  P,  indicates  the  price  level  of  work- 
men's consumption,  and  the  index,  T,  means  an  index  for 
workmen's  real-wages.  Any  special  form  of  price  index  now 
implies  a  correlative  special  form  of  real-wages  index. 

Again,  if  we  are  studying  statistics  of  capital  such  as  in 
Giffen's  Growth  of  Capital,  we  have  2pQ  as  the  value  of  capi- 
tal, the  p's  being  the  prices  of  different  forms  of  capital  and 
the  Q's,  their  quantities.  For  every  special  form  of  price 
index  number,  P,  representing  the  price  level  of  capital, 
there  will  be  a  correlative  special  index  of  capital  showing 
the  real  "growth  of  capital"  as  distinct  from  its  mere  money 
value.  Such  an  index  seems  seldom  to  have  been  employed.^ 
Yet  it  is  evidently  advisable  to  distinguish  between  an  ap- 
parent increase  of  capital  due  to  inflated  prices  and  a  real 
increase,  as  would  be  shown  by  such  an  index  as  here 
suggested. 

*  See  Giffen,  Growth  of  Capital,  London  (George  Bell  and  Sons), 
1889,  pp.  50-54,  where  allowance  is  made  for  changes  in  the  price 
level.  Index  numbers  of  the  Economist,  of  Sauerbeck,  and  of 
Soetbeer  are  cited.  Professor  J.  S.  Nicholson  has  advocated  such 
a  capital-standard  in  the  Journal  of  the  Royal  Statistical  Association, 
March,  1887,  pp.  152  ff.  This  method  is  discussed  by  Edgeworth, 
Report  of  the  British  Association,  1887,  p.  276. 


Sec.  3]  APPENDIX  TO   CHAPTER   X  393 

We  see,  therefore,  that  wherever  prices  and  quantities  are 
united,  we  have  the  requisite  conditions  for  constructing 
correlative  pairs  of  index  numbers,  one  index  in  each  pair 
relating  to  prices,  and  the  other  to  quantities. 

We  shall,  however,  for  convenience,  continue  to  employ 
the  magnitude  7",  rather  than  Q,  and  to  refer  to  it  as  a 
"trade"  index. 


§  4.  Review  of  44  Formulce,  heading  the  Table  Columns 

We  shall  now  briefly  review  the  formulae  of  the  table  of 
selected  index  numbers.  Each  even-numbered  formula  is 
best  regarded  as  derivable  from  the  odd-numbered  formula 
at  its  left  as  its  antithesis.  The  odd  formulae  are  those  con- 
structed directly  for  the  p's  without  reference  to  any  average 
for  the  Q's;  the  even  are  constructed  indirectly  by  refer- 
ence to  some  average  first  assumed  for  the  Q's.  The  latter 
are  what  Walsh  had  in  mind  under  the  name  of  "  double 
weighting." 

Formula  (1)  is  simply  the  ratio  of  the  sums  of  prices.  It 
may  also  be  considered  as  the  ratio  of  the  averages  of  prices 
in  the  two  years  considered,  as  is  evident  by  writing  it,  — 

— -,  where  n  is  the  number  of  commodities  employed. 
n 

This  formula  was  used  by  Dutot  in  1738,^  and  has  been 
used  recently  by  Bradstreet,^  who  applied  it  practically. 

Although  it  is  a  ratio  of  average  prices,  it  may  also  be 
thrown  into  the  form  of  a  weighted  arithmetical  average  of 

the  price  ratios,  ^,  ^,  ^,  etc.,  as  the  following  transfor- 
Po    Po    p  0 

mation  shows :  — 

1  See  Walsh,  Measurement  of  General  Exchange  Value,  New  York 
(Macmillan),  1901,  pp.  534,  553. 
*  BradstreeV s  Journal  from  1895. 


+ 


394         THE   PURCHASING   POWER   OF  MONEY     [Append.  X 

Spi  ^  pi  +  p'l  +  p''i  +  — 
2po     Po  +  p'o  +  p"o+  ••• 

Po  +  p'o  +  p"o+  ••• 

The  formula  in  this  last  form  is  evidently  the  weighted  arith- 
metical average  of  the  ratios  in  parenthesis,  the  weights  be- 
ing the  prices  po,  p'o,  p"o,  •••  of  the  year  0.  A  change  in 
the  units  of  quantity  for  the  various  goods  would  change 
these  prices;  thus  a  change  from  ounces  to  pounds  would 
multiply  the  number  expressing  price  by  sixteen.  Such  a 
change  in  any  price,  such  as  po,  would  entirely  change  the 
relative  importance  of  the  "  weights,"  po,  p'o,  etc.  Conse- 
quently this  system  of  weighting  is,  as  Walsh  says,  quite 
accidental  or  haphazard.^ 

The  same  formula  is  also  a  harmonic  average,  as  the  follow- 
ing transformations  show :  — 


2pl 

Spo 

_P1  +  P'l+ 

Po  +  p'o  + 

Pl  +  P 

'l+ 

'  P'©+P' 

'fp' 

V 

1 

0.1... 

~<f>^' 

<^^ 

")-  - 

Pl  +  p'l+  ••• 

The  last  expression  is  evidently  the  reciprocal  of  a  weighted 
arithmetical  average  of  the  price  ratios  in  parenthesis.     But 

these  price  ratios  are  the  reciprocals  of  (— )>  (/)>  (    /T  )>  ^*^' 
In  other]  words,  the  formula  is  the  reciprocal  of  a  weighted 
*  Walsh,  op.  cit.,  pp.  81  and  82. 


Sec.  41  APPENDIX  TO   CHAPTER  X  395 

arithmetical  average  of  the  reciprocals  of  the  ratios  — ,  etc. 

It  is  therefore  the  weighted  harmonic  average  of  these  ratios 

— ,  etc.,  the  weights  being  pi,  p/,  etc.,  or  the  prices  of  the 
Po 

year  1. 

In  short,  formula  (1)  is  both  an  arithmetical  and  a  har- 
monic average  of  ^,  ^\  etc.,  the  weights  being,  in  the  first 
Po    p  0 

case,  the  terms  of  the  denominator,  and  in  the  second,  those 
of  the  numerator. 

We  have  seen  that  formula  (1)  in  the  table,  although 
primarily  a  ratio  of  averages  of  prices,  may  be  also  con- 
sidered as  an  average  of  ratios  of  prices  with  arbitrary 
weighting. 

Conversely  we  may,  if  we  choose,  regard  every  average  of 
ratios  as  a  ratio  of  averages  by  assuming  arbitrary  units  for 
measuring  commodities.  It  is  evident  that,  if  the  unit  of 
measure  is  increased  in  any  ratio,  the  number  expressing 
the  price  is  decreased  in  the  inverse  ratio.  If,  therefore,  we 
change  the  unit  of  measure  of  a  commodity  the  price  of 
which  is  at  first  expressed  by  pi  by  dividing  by  the  ratio  po, 

this  price  becomes  ^.     Thus  ^  may  be  considered  to  be  a 
Po  Po 

price  as  well  as  a  price  ratio.    Hence  an  average  of  ^,  ^,  ^, 

Po   Po  p  0 

etc.,  may  be  regarded  as  an  average  of  prices.     The  new 

units,  instead  of  being  pounds,  yards,  etc.,  are  dollars-worth-in- 

the-hase-year.    With  these  units,  the  price  in  the  base  year  is 

unity,  for  dividing  the  price,  po,  in  the  original  units  by  the 

factor  Po,  we  obtain  unity. 

Hereafter,  however,  we  shall  treat  all  index  numbers  as 
averages  of  price  ratios. 

It  is  interesting  to  note  that  the  antithesis  of  Dutot's  or 
Bradstreet's  formula  (No.  2),  found  by  dividing  the  frac- 

tioJi  -^^  by  the  correlative  formula  for  Qi,  viz.,  -^,  turns 
SpoQo  2^0 


396         THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

out  to  be  that  advocated  by  Drobisch,^  and  earlier  by  Sir 
Rawson-Rawson .  "^ 

Formula  (3)'  is  evidently  the  familiar  simple  arithmetical 
average,  — 

^W  or  Po^P^o^       ^Vr' 


Formula  (4),  the  antithesis  of  formula  (3),  gives,  as  the 
average  price  ratio,  the  ratio  of  total  values  SpiQi  /  SpoQo 
corrected  for  change  in  the  Q's  by  division  by  the  arith- 
metical average  ratio  of  the  Q's. 

Hereafter  the  even-numbered  formulae,  being  antitheses  of 
the  preceding  odd  formulae,  will  be  passed  over  unless  there 
is,  in  any  case,  special  reason  for  mention. 

^  See  M.  W.  Drobisch,  "Ueber  Mittelgrossen  und  die  Anwend- 
barkeit  derselben  auf  die  Bereehnung  des  Steigens  und  Sinkens  des 
Geldwerthes  "  (Berichte  liber  die  Verhandlungen  der  Koniglich  sdchs- 
ischen  Gesellschaft  der  Wissenschaften  zu  Leipsig ;  Mathematisch- 
physische  Classe,  Band  XXIII,  1871,  pp.  25-48).  Also  "  Ueber  die 
Bereehnung  der  Veranderungen  der  Waarenpreise  und  des  Geld- 
werthes "  (Jahrbiicher  fur  N ational-oekonomie  und  Statistik,  1871, 
Band  XVI,  pp.  143-156)  ;  and  "  Ueber  einige  Einwiirfe  gegen  die  in 
diesen  Jahrbiichern  veroffentlichte  neue  Methode,  die  Verander- 
ungen der  Waarenpreise  und  des  Geldwerthes  zu  berechnen  '* 
(ibid.,  1871,  Band  XVI,  pp.  416-427).  See  also  Walsh,  op.  ciL, 
pp.  97-99,  where  the  method  is  explained. 

2  See  Edgeworth,  Report  of  the  British  Association  for  the  Ad- 
vancement of  Science,  1889,  p.  152.  Sir  Rawson-Rawson' s  sug- 
gestion, as  developed  by  Edgeworth,  was  to  divide  the  value  of 
exports  (or  imports)  by  the  tonnage  of  exports  (or  imports)  and 
consider  the  result  as  an  index  number  of  prices  of  exports  (or  im- 
ports). The  suggestion  was  made  not  for  any  theoretical  virtues, 
but  because  of  the  practical  ease  of  computation.  Edgeworth 
compares  the  results  of  Rawson's  rough  and  ready  method  with  the 
more  exact  method  of  Giffen  by  actual  figures  for  1886  compared 
with  1885,  and  finds  substantial  agreement. 

"  For  a  statement  of  the  history  of  this  formula  from  Carli  to  the 
present,  see  Walsh,  op.  cit.,  p.  534. 


Sec.  4]  APPENDIX  TO   CHAPTER   X  397 

Formulae  (5),  (7)\  and  (9)^  are  respectively  the  simple 
harmonic,  simple  geometric,  and  simple  median  averages. 
We  note  that  the  antithesis  of  (7),  viz.  (8),  is  one  proposed  by 
Nicholson  and  Walsh  .^ 

Formula  (11)*  resembles  Bradstreet's,  except  that  the  in- 
troduction of  the  Q's  as  multipliers  prevents  the  weighting 
from  being  arbitrary  ;  for  the  weights  poQi,  etc.,  unlike  the 
weights  po,  etc.,  are  uninfluenced  by  a  change  in  the  units 
of  measurement  for  commodities.  Whether  an  article  be 
measured  in  pounds  or  ounces  will  not  affect  the  value  of  a 
given  amount  of  it.  The  following  transformations  show 
that  the  formula  is  a  weighted  arithmetic  mean  :  — 

^PiQ^_PiQi  +  p'^Q\+  ••• 
SpoQi    PoQi-\-p'oQ'i+  '•• 


+ 


The  last  expression  is  evidently  a  weighted  arithmetic 
average  of  the  price  ratios  in  the  parentheses,  the  weights 
being  poQi,  p'oQ'i,  etc.,  i.e.  the  values  of  the  quantities  in  the 
year  1  reckoned  at  the  prices  of  year  0. 

But  the  same  formula  is  also  a  harmonic  average,  as  may 
be  seen  by  transforming  the  denominator  instead  of  the 
numerator  as  was  done  for  formula  (1).  It  is  a  weighted 
harmonic  average,  the  weights  being  piQi,  p\Q'i,  etc.,  or  the 
values  in  the  year  1. 

In  short,  formula  (11)  or  —^  is,  like  formula  (1),  both  a 


SpoQi 


weighted  arithmetical  and  a  weighted  harmonic  average  of 

^  See  Jevons,  Investigations  in  Currency  and  Finance,  London 
(Maemillan),  1884  ;  Edgeworth,  Reports  British  Association,  1887,  8, 
9;  Walsh,  op.  cit.,  pp.  229  ff. 

2  See  Edgeworth,  Reports  British  Association,  1887,  8,  9,  esp. 
1888,  pp.  206  ff. 

'  Walsh,  op.  cit.,  p.  548. 

*  For  Formulae  11  and  12  there  exists  a  large  literature.  See 
Walsh,  op.  cit.,  esp,  pp.  191  ff.,  and  pp.  539  ff. 


398  THE   PURCHASING   POWER   OF  MONEY      [Append,  X 

^>     /  >  ^>  6tc.,  but  the  weights  are  different  in  the  two 
Po    Po    p  0 

cases. 

(11)  has  the  interesting  property  that  its  antithesis  (12)  is 
of  the  same  form  except  that  the  subscripts  for  Q  are  now  0 
in  place  of  1.  Similar  reasoning  shows  that  this  formula  (12) 
is  also  both  an  arithmetical  and  an  harmonic  average,  weighted 
according  to  the  terms  in  its  denominator  and  numerator 
respectively. 

These  two  formulae,  (11)  and  (12),  seem  to  be  the  favorites 
among  writers  on  Index  Numbers.  Since  the  shortcomings 
of  one  are,  in  some  cases,  not  shortcomings  of  the  other,  there 
have  been  many  attempts  to  combine  them  into  some  com- 
posite. No.  (13),^  for  instance,  is  their  simple  arithmetical 
average.  The  antithesis  of  (13),  viz.  (14),  turns  out  to  be  the 
simple  harmonic  average  of  (11)  and  (12).  Number  (15)  is  the 
simple  geometric  average  of  (11)  and  (12).  This  formula  (15) 
has  the  distinction  of  being  identical  with  its  own  antithesis 
(16).  Numbers  (17),  (19),  (21),  and  (23)  are  other  attempts 
at  combining  (11)  and  (12),  not  by  averaging  them,  as  was 
the  case  with  (13)  and  (15),  but  by  averaging  their  coefficients, 
viz.,  Qi  and  Qq,  Q\,  and  Q'o,  etc.  Two  antitheses  of  these, 
namely  (18)  and  (22),  turn  out  to  be  formulae  proposed  by 
Walsh,  and  a  third  (24)  to  be  one  proposed  by  Julius  Lehr.^ 

We  have  seen  that  the  formulae  (11)  and  (12)  considered 
as  arithmetical  averages  have  for  weights 

PoQi,  p'oQ'i,  p"oQ"i,  etc.,  for  No.  (11), 

and  poQo,  p'oQ'o,  p"oQ"o,  etc.,  for  No.  (12). 

We  next  use  weights 

PiQi,  p'lQ'i,  p'\Q'\,  etc.,  for  No.  (25), 

and  piQo,  p'xQ'o,  p"iQ"q,  etc.,  for  No.  (27), 

^  For  references  to  literature  concerning  this  and  many  others 
among  the  remaining  formulae  of  the  table  (col.  13-44),  see  Walsh, 
op.  cit. 

^  Beitrdge  zur  Statistik  der  Preise,  Frankfurt-a.-M,  1885  (p.  11  and 
pp.  37-42  for  the  method).  The  method  is  explained  in  Walsh, 
Measurement  of  General  Exchange-Value,  pp.  386-388. 


Sec.  4]  APPENDIX  TO    CHAPTER  X  399 

thus  completing  the  four  permutations  of  the  subscripts,  01, 
00,  11,  10.  Number  (29)  represents  a  weighted  arithmetical 
average  in  which  the  weights  are  derived  from  other  con- 
siderations than  the  product  of  the  prices  and  quantities  of 
the  base  year  (1).  An  instance  is  the  method  employed  in 
some  of  the  tables  in  the  "Aldrich  Report,"  ^  the  weights 
being  the  percentage  of  consumption  of  various  kinds  in 
workingmen's  budgets  without  reference  to  the  base  year  or 
any  other  particular  year. 

Numbers  (31)  and  (33)  are  weighted  harmonic  means  in 
which  the  weights  instead  of  being 

PiQi,  etc.,  as  in  (11), 
or  piQo,  etc.,  as  in  (12), 

are  poQi,  etc.,  for  (31), 

and  poQo,  etc.,  for  (33), 

thus  completing  for  harmonic  averages  the  same  permuta- 
tions of  subscripts  as  before  for  arithmetical  averages.  We 
see  then  that  the  odd  formulae  (11)  to  (33)  inclusive  are 

merely  arithmetical  averages  or  harmonic  averages  of  ^, 

etc.,  or  else  averages  or  mixtures  of  such  averages. 

Numbers  (35),  (37),  (39),  (41)  are  various  forms  of 
weighted  geometric  averages  of  those  price  ratios,  the 
weights  being 

PiQi,  etc.,  for  (35). 

poQo,  etc.,  for  (37). 

PiQo,  etc.,  for  (39). 

PoQi,  etc.,  for  (41). 

Number  (43)  is  the  ratio  of  the  weighted  geometric  aver- 
age of  the  prices  in  years  1  and  0,  the  weights  being  piQi,  etc., 
for  year  1  and  poQo,  etc.,  for  year  0. 

*  Report  on  Wholesale  Prices,  Senate  Report  1394,  2d  Sessioiii 
52d  Congress,  1893. 


400         THE   PUKCHASING   POWER  OF  MONEY      [Append.  X 

It  will  be  seen  that  all  of  the  44  formulae  selected  for  the 
table  are  based  on  a  few  simple  principles  of  averaging. 
Most  are  arithmetic,  harmonic,  or  geometric  averages  or 
their  combinations.  Needless  to  say,  numerous  other  and 
more  complicated  forms  might  be  constructed. 

§  5.     Review  of  Eight  Tests,  heading  the  Table  Rows 

Having  reviewed  the  headings  of  the  vertical  columns  of 
the  table,  we  have  next  to  note  the  headings  of  the  horizon- 
tal rows.  These  headings  are  the  eight  tests  of  index  num- 
bers. The  first  six  tests  are  arranged  in  pairs,  the  odd  being 
expressed  in  terms  of  prices  and  the  even  in  terms  of 
quantities. 

The  Eight  Tests  for  a  Good  Index  Number 

The  eight  tests  are  intended  to  include  all  the  tests  which 
have  been  hitherto  applied  in  the  study  of  index  numbers 
and  some  others.     They  are: 

1.  Test  of  proportionality,  as  to  prices. 

2.  Test  of  proportionaUty,  as  to  trade. 

3.  Test  of  determinateness,  as  to  prices. 

4.  Test  of  determinateness,  as  to  trade, 

5.  Test  of  withdrawal  or  entry,  as  to  prices. 

6.  Test  of  withdrawal  or  entry,  as  to  trade. 

7.  Test  by  shifting  base,  both  as  to  prices  and  as  to  trade. 

8.  Test  by  shifting  unit  of  measurement,  both  as  to  prices 
and  as  to  trade. 

We  shall  first  define  each  of  these  tests  in  general  terms 
and  then  proceed  to  illustrate  them  by  actual  applications. 

1.  Test  of  proportionality  as  to  prices.  A  formula  for  the 
price  index  should  be  such  that  the  price  index  will  agree 
with  all  individual  price  ratios  when  these  all  agree  with 
each  other.  Thus,  if  in  1910  the  price  of  everything  is  10  per 
cent  higher  than  in  1909,  the  index  number  should  register 
10  per  cent  higher. 


Sec.  51  APPENDIX  TO   CHAPTER   X  401 

2.  Test  of  proportionality  as  to  trade.  Likewise  the  cor- 
relative formula  for  the  trade  index  should  be  such  that  the 
trade  index  will  agree  with  all  individual  trade  ratios  when 
these  all  agree  with  each  other. 

3.  Test  of  determinateness  ac  to  prices.  A  price  index  should 
not  be  rendered  zero,  infinity,  or  indeterminate  by  an  individ- 
ual price  becoming  zero.  Thus,  if  any  commodity  should  in 
1910  be  a  glut  on  the  market,  becoming  a  "  free  good,"  that 
fact  ought  not  to  render  the  index  number  for  1910  zero. 

4.  Test  of  determinateness  as  to  trade.  The  correlative  trade 
index  should  not  be  rendered  zero,  infinity,  or  indeterminate 
by  an  individual  quantity  becoming  zero.  Thus,  if  any  com- 
modity should  go  completely  out  of  use  in  1910  so  that  its 
quantity  exchanged  becomes  zero,  that  fact  ought  not  to 
render  the  trade  index  for  1910  indeterminate. 

5.  Test  of  withdrawal  or  entry  as  to  prices.  A  price  index 
should  be  unaffected  by  the  withdrawal  or  entry  of  a  price 
ratio  agreeing  with  the  index.  Thus,  if  the  price  index  of  a 
certain  number  of  goods,  not  including  sugar,  should  be  105 
in  1910  as  compared  with  1900,  and  the  price  of  sugar  itself 
should  be  105  in  1910  as  compared  with  1900,  then  the  in- 
clusion of  sugar  in  the  calculation  of  the  index  number  ought 
not  to  change  the  index  from  105. 

6.  Test  of  withdrawal  or  entry  as  to  trade.  The  correlative 
trade  index  should  be  unaffected  by  the  withdrawal  or  entry 
of  a  quantity  ratio  agreeing  with  the  index. 

7.  Test  hy  changing  base.  The  ratios  between  various  price 
indexes  (and  therefore  also,  as  we  shall  see,  the  ratios  between 
the  correlative  trade  indexes)  should  be  unaffected  by  revers- 
ing or  changing  the  base.  Thus,  if  the  index  number  for  1910 
is  twice  that  for  1900,  when  calculated  on  the  basis  of  1860, 
it  should  remain  twice,  when  calculated  on  the  basis  of  1870. 

8.  Test  hy  changing  unit  of  measurement.  The  ratios  be- 
tween various  price  indexes  (and  therefore  also,  as  we  shall 
see,  the  ratios  between  the  correlative  trade  indexes)  should 
be  unaffected  by  changing  any  unit  of  measurement.  Thus, 
if  the  index  number  for  1910  is  twice  that  for  1900  when  coal 

2d 


402    THE  PURCHASING  POWER  OF  MONEY  (Append.  X 

is  measured  by  the  ton,  it  should  remain  twice,  when  coal  is 
measured  by  the  pound. 

The  statements  of  tests  7  and  8  are  expressed  in  each  case 
both  as  to  prices  and  quantities;  in  these  cases  it  was  im- 
plied that  what  holds  true  of  price  indexes  holds  true  also  of 
trade  indexes,  and  vice  versa.  To  show  this  reciprocal  rela- 
tion for  test  7  (base  shifting),  let  the  price  index  for  year  1 
in  terms  of  year  0  be  designated  by  Pi,  o  instead  of  by  Pi  as 
heretofore,  in  order  that  the  base  year  may  be  specifically 
designated,  and  let  us  compare  years  1  and  2  by  using  first 
year  0  as  a  base  and  then  (say)  year  8.     If  the  base-shifting 

P         P 

test  is  fulfilled  for  the  P's,  i.e.  if  — ^^  =  — ^ ,  we  are  to  prove 

P2,  0        P2,  8 

that  the  corresponding  relation  is  also  true  for  the  T's,  viz. 
that 

Ti,  0  _  Ti,  s 

Tz,  0        T2,  8 

We  know  that  Ti,  0  =  %^  •  (1) 

PljO 


m      _  -*/'2V2 
i  2, 0       p 

■t  2, 0 

(2) 

Jt  lj8  ' 

(3) 

i  2,  8  -    p 

X^2,  8 

(4) 

Divide  (1)  by  (2)  and  (3)  by  (4).    The  quotients  are 

Ti,o_fMQyYP2,o\ 
2^2,0      \.MQ2APi,oJ' 

^2,8     y^PiQiAPuJ 

Comparing  the  right  sides  of  these  equations,  we  find  that 
the  "  2  "  ratios  are  identical  in  the  two  cases,  and  we  know 
that  the  P  ratios  are  equal  by  hypothesis.    Consequently 


Sec.  5]  APPENDIX  TO   CHAPTER  X  403 

the  entire  right  sides  of  the  two  equations,  and  therefore 
the  left  sides,  are  also  equal,  and  this  is  what  was  to  be 
proved.     The  converse  reasoning  is  also  evident. 

Like  the  base-shifting  test,  the  unit-shifting  test,  No.  8, 
cannot  apply  to  prices  without  applying  also  to  quantities, 
and  vice  versa.     To  show  this  we  employ  the  equation  T  = 

-^^'     Evidently  the  numerator  of  the  right  side  of  this 

equation  is  unaffected  by  a  change  of  unit.  For  instance, 
if  coal  should  be  measured  in  ounces  instead  of  tons,  thus 
greatly  increasing  the  number  (say  Q)  representing  its  quan- 
tity, the  value  {pQ)  will  not  be  disturbed,  since  the  number 
(p)  representing  the  price  will  be  correspondingly  diminished. 
Consequently,  if  the  denominator  (P)  meets  the  correspond- 
ing test,  i.e.  is  likewise  unaffected  by  a  change  in  unit,  the 
quotient  (T)  must  be  unaffected.  That  is,  if  the  unit-shift- 
ing test  is  met  for  P,  it  must  be  met  for  T.  As  the  con- 
verse reasoning  also  apphes,  the  proposition  is  proved. 

As  will  have  been  noted,  the  first  six  tests  are  expressed 
alternately  in  terms  of  prices  and  in  terms  of  quantities. 
We  now  wish  to  point  out  that  those  expressed  in  terms  of 
prices  have  a  significance  for  quantities  also,  and  that  those 
expressed  in  terms  of  quantities  have  a  significance  for  prices 
as  well.  That  is,  all  the  tests  have  significance  both  as  to 
prices  and  as  to  quantities. 

To  emphasize  this  fact,  which  is  important,  let  us  note  the 
price  significance  of  each  test.  Since  the  price  significance 
of  tests  1,  3,  5,  7,  8  is  evidently  expressed  in  the  statement 
of  the  test,  we  have  left  merely  to  express  the  price  signifi- 
cance of  tests  2,  4,  6. 

Test  2  tells  us  that  if  all  the  trade  ratios  agree,  their  index 
should  agree  with  them ;  that  is, 

if  Qi  _  Q 1  _  Q  1  _  ...  _  t 

T 
then  also  should     — ^  =  k. 


404  THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

The  question  now  before  us  is,  assuming  this  condition  to  hold 
as  to  the  Q's,  what  condition  holds  true  as  to  the  p's.  The 
answer  evidently  is:  — 


^PiQ 


[obtained  by  substituting  kQz  for  Qi,  kQ'2  for  Qi,  etc.,  and  kTi 
for  Tx]  =  ^PiQa  =  SpiQi  _ 

2P2Q2     SpoQi 
The  last  form  is  derived  from  the  next  to  the  last  by  multi- 
plying both  numerator  and  denominator  by  k  and  then  sub- 
stituting Qi  for  kQi,  Q'l  for  kQ'2,  etc. 

The  resulting  two  formulae  for   — ^  express  test  No.  2  in 

terms  of  the  conditions  to  which  prices  must  conform. 
These  formulae  will  be  recognized  as  those  discussed  in  §  7 
of  the  Appendix  to  Chapter  II,  the  significance  of  which  was 
there  explained.  It  was  there  shown  that  a  change  in  M,  or 
a  change  in  F,  or  a  uniform  change  in  all  the  Q's,  or  any 
combination  of  these  changes  will,  through  the  equation  of 
exchange,  affect  the  price  level  in  the  maimer  expressed  by 
the  formula:  — 

El  ^  SpiQi  ^  SpiQz . 

P2      27?2Qi      ^paQo 

Thus  the  equation  of  exchange  itself  prescribes  test  No.  2; 
for  the  fundamental  theorems  which  the  equation  of  ex- 
change has  taught  us  are  that  prices  vary  directly  as  M  and 
as  the  F's  and  inversely  as  the  Q's;  and  the  only  forms  of 
index  numbers  which  will  faithfully  reflect  these  changes,  i.e. 
will  vary  directly  with  M  and  inversely  with  the  Q's  (assum- 
ing that  all  Q's  vary  in  unison),  are  those  forms  of  index 
numbers  which  conform  to  test  No.  2.  Any  other  form  of  in- 
dex number,  when  M  (and  M')  increased  50  per  cent  and  there 
was  no  change  in  F's  or  Q's,  might  register  a  rise  of  49  per  cent 


Sec.  5]  APPENDIX  TO   CHAPTER  X  405 

or  51  per  cent.  That  is,  no  other  forms  of  index  numbers  will 
enable  us  to  say  that  when  the  quantity  of  money  changes,  the 
velocity  of  circulation  and  the  Q's  remaining  the  same,  the 
index  number  of  prices  will  vary  proportionately.  No  other 
forms  will  enable  us  to  state  the  corresponding  theorem 
as  to  the  effect  of  a  change  in  velocity  or  of  a  (uniform) 
change  in  the  Q's.  But  these  theorems  are  fundamental.  The 
very  concept  of  an  index  number  is  that  it  shall  replace  the 
divergent  individual  variations  and  enable  us  to  state  of  its 
proportionate  changes  the  same  theorems  which  hold  true 
when  prices  all  change  alike. 

Test  No.  2  is  therefore  of  such  fundamental  importance 
that  we  may  profitably  pause  a  moment  to  restate  it  in 
words.  To  be  concrete,  let  us  suppose  two  years,  1900  and 
1910.  Let  us  assume  that  the  quantity  of  every  kind  of 
goods  sold  in  1910  is  (say)  exactly  double  the  quantity  sold 
in  1900.  Then  the  only  proper  ndex  number  showing 
the  level  of  prices  in  1910  (year  1)  as  compared  with  the 

level  of  prices  in  1900  (year  0)  is       ^   ^  the  ratio  of  the  total 

value  of  the  goods  sold  in  1910  to  what  that  value  would 
have  been  at  the  prices  of  1900 ;  or,  what  amounts  to  the 

same  thing,  it  is  ~~^  the  ratio  of  what  the  total  value  of 

the  goods  sold  in  1900  would  have  been  at  the  prices  of  1910 
to  what  it  actually  was  at  the  prices  of  1900. 

Of  the  44  formulae  in  the  table,  only  the  following  reduce 
to  the  required  formula  when  the  Q's  change  uniformly: 
(2)  of  Drobisch,  (4),  (6),  (8),  (10),  (11),  (28),  (30),  (34),  (38), 
(40).  All  these  are  even-numbered  except  formula  11. 
Several  others  will  reduce  to  the  required  formula,  provided 
one  of  the  years  compared  is  the  base  year. 

The  formulae  of  the  tables  which  fail  to  meet  test  2  at  all 
would  not  even  allow  us  to  say  of  MV+M'V'=PT  that  if 
all  the  Q's  remain  the  same,  T  will  remain  constant  and 
P  will  vary  as  the  other  side  of  the  equation.  For  these 
formulae  T  fails  as  a  true  index  of  the  Q's,  and  its  error 


406  THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

in  one  direction  implies  a  corresponding  error  in  P  in  the 
opposite  direction. 

Test  2  seems  therefore  in  some  respects  the  most  important 
of  all  the  eight  tests  for  prices;  although  primarily  it  was 
not  stated  in  terms  of  prices,  but  in  terms  of  quantities.  It 
is  the  only  test  which  indicates  the  kind  of  weighting  re- 
quired. It  completely  prescribes  the  conditions  which, 
while  permitting  any  individual  changes  in  prices,  however 
divergent,  enable  us  to  say  that  a  change  in  M  or  the  two 
F's  or  in  all  the  Q's  in  a  given  ratio  will  affect  prices  "  on 
the  average  "  in  that  same  ratio  (directly,  of  course,  for  the 
ilf' s  and  F's  and  inversely,  for  the  Q's). 

Test  2  in  fact  points  out  the  true  form  of  the  index  num- 
ber of  prices  as  prescribed  by  the  equation  of  exchange  under 
all  possible  circumstances  except  when  the  Q's  vary  in  un- 
equal proportions.  It  also  points  to  the  proper  weights 
required.  These  weights  may  be  said  to  depend  either  on 
the  Qi's  or  on  the  QqS,  interchangeably.  The  formula  sug- 
gested by  the  Q\S  is  formula  1 1 ;  that  suggested  by  the  QqS 
is  formula  12.  Either  will  be  perfectly  satisfactory  when  the 
Qi's  and  Qo's  are  proportional,  while  when  they  are  not,  their 
discrepancy  is  negligible.  When  the  Q's  vary  unequally, 
however,  there  seems  to  be  no  perfectly  satisfactory  formula. 
Under  these  circumstances  the  two  systems  of  weights  — 
one  in  terms  of  Qi's,  the  other  in  terms  of  Qo's  —  conflict 
with  each  other.  But  the  conflict  has  been  shown  by  Edge- 
worth  ^  to  be  slight.  In  fact,  the  weights  are  of  much  less 
importance  in  determining  an  index  number  of  prices  than 
the  prices  themselves. 

The  discussion  of  test  2  will  be  resumed  later  when  in  §  7 
we  come  to  compare  the  various  forms  of  index  numbers. 

*  Report  of  the  British  Association  for  the  Advancement  of  Science 
for  1887,  pp.  288-292  and  for  1888,  pp.  197-198,  200,  202,  203,  206. 
Edge  worth  shows  in  the  case  specified  by  him  that  an  "error"  in  the 
iseights  only  makes  an  "error"  one  twentieth  as  great  in  the  re- 
sultant index  number,  while  an  "error"  in  the  prices  themselves 
makes  an  "error!!  in  the  resultant  index  number  one  fourth  or  fifth 
as  great. 


Sec.  5] 


APPENDIX  TO   CHAPTER   X 


407 


Tests  Algebraically  Stated  for  the  General  Case  of  any 

TWO    YEARS    compared     AS    TO     PRICES     AND    TRADE.       (FOR    THE 

Special  Case  when  one  of  the  two  years  is  a  base  year, 
substitute  "0"  for  "2.") 


Test  1, 
Proportionality  as 
top's 

Test  2, 
Proportionality  as 
to  C'8 

Test  3, 
Determinateness 
as  to  p's 

Test  4, 
Determinateness 
as  to  Q's 

Test  5, 
By  withdrawal  or 
entry  as  top's 


Test  6, 
By  withdrawal  or 
entry  as  to  Q's 


Teat  7, 
By  changing  base 


Test  8, 
By  changing  units 
of  measurement 


Pi  =  0  or 
Pi  =  0,  etc. 


$,  =  0  or 
Qj  =  0,  etc. 


Pz     Pi 


Pi     P't ' 


Base  changed  from 
"0"  to  "8"  Chang 
ing: 

A.  0  to  Pi,, 
A,  0  to  P„  , 
Tx,  0  to  2\,  , 
Ti,  0  to  r,, , 

Qjand  pi  changed  in 
inverse  ratio 


A 


Pj  and  Pj  determinate 
and  not  zero  nor  in 
finity 

P-i  and  P,  determinate 
and  not  zero  nor  in- 
finity 


Th«  Test  Kkqttibes  that 
(as  top's)  (as  to  Q'&) 


(Primes  signify  that 
Pi.  Pi>  Qi,  Qi  are 
excluded ;  absence  of 
primes  signifies  they 
are  included.) 


P\_^P\Q\.  7\ 
P\      '^P\Q\  '  7i 
(Primes    and     their 
absence    signify     as 
above.) 


-^  unchanged 


Tj  and  7*,  determinate 
and    not    zero    nor 

infinity 

Ti  and  T,  determinate 
and  not  zero  nor 
infinity 

T'i     ^p\Q\  .  Pt 

T\  S-p'tQ't  ■  P, 
(Primes  signify  p,. 
Pi,  Q\,  Qt  are  ex- 
cluded ;  absence  of 
primes  signifies  they 
are  included.) 


=  k 


T'._ 

(Primes  and  their 
absence  signify  as 
above.) 


p  unchanged 


408         THE    PURCHASING    POWER   OF   MONEY       [Ai  pend.  X 

As  to  test  4,  this  states  that  if  an  individual  quantity  be- 
comes zero  this  fact  should  not  render  the  quantity  or  trade- 
index  zero,  infinity,  or  indeterminate.  But  according  as  the 
index  does  or  does  not  become  zero,  infinity,  or  indetermi- 
nate, will  the  price  index  become  or  not  become  infinity,  zero, 
or  indeterminate  respectively.  This  is  clear  from  the  rela- 
tion Pi  =  -VMl .     Hence  test  4  possesses  a  significance  as  to 

prices  similar  to  that  which  it  possesses  as  to  quantities. 

The  price  significance  of  test  6  is  more  complex  and  of  no 
apparent  importance.  Its  statement  is  included  in  the  ex- 
planatory table  on  page  407.  In  the  preceding  table  of 
44  index  numbers  the  "  score "  for  test  6  is  bracketed  to 
indicate  that  it  has  no  important  price  significance,  and  is 
to  be  omitted  in  the  totals. 

Mutatis  mutandis,  each  of  the  tests  expressed  in  terms  of 
prices  (tests  1,  3,  5)  has  a  significance  as  to  quantities  also. 

The  preceding  explanatory  table  exhibits  in  algebraic  terms 
both  hjrpothesis  and  conclusion  for  each  of  the  eight  tests 
with  respect  both  to  prices  and  quantities. 

§  6.    The  Interior  of  the  Table;  Column  11  in  Particular 

We  have  reviewed  briefly  the  headings  of  the  table,  includ- 
ing both  those  of  the  vertical  columns  and  those  of  the  hori- 
zontal rows.  Their  relations  to  each  other  are  contained  in 
the  interior  of  the  table.  The  object  of  the  table  is  to  show 
the  degree  of  conformity  of  the  44  various  formulae  for  P 
(and  their  correlates  for  T)  to  the  eight  tests.  In  spite  of 
all  the  mathematical  ingenuity  spent  by  many  writers  in 
devising  index  numbers,  no  known  formula  and  apparently 
no  possible  formula  will  meet  all  eight  of  the  tests. 

For  each  test  we  note  three  possible  degrees  of  conformity. 
It  may  be  fulfilled  by  any  particular  formula  in  three  de- 
grees of  conformity  or  nonconformity:  (1)  completely,  (2) 
partially,  or  (3)  not  at  all.  These  three  degrees  are  indicated 
in  the  table  which  follows,  by  the  numbers  1,  |^,  0  respec- 


Sec.  6]  APPENDIX  TO   CHAPTER   X  409 

tively.  A  test  is  completely  fulfilled  by  index  numbers  for 
any  two  years  whatever  (as  year  1  and  year  2).  A  test  is 
partially  fulfilled  if  it  is  fulfilled  by  index  numbers  for  two 
years,  one  of  which  is  the  base  year  (year  0),  Thus  the 
former  relates  to  the  general  case,  the  latter  to  a  particular 
case.  Since  the  general  includes  the  special,  if  the  test  is 
fulfilled  in  general  it  is  fulfilled  in  particular;  the  converse 
is  not  necessarily  true.  But  if  the  test  is  not  fulfilled  in  the 
particular  case,  it  is  not  fulfilled  in  general;  the  converse  of 
this  proposition  is  not  necessarily  true.  In  short,  an  afl&rma- 
tive  answer  to  the  question  of  complete  conformity  carries 
with  it  an  affirmative  answer  to  the  question  of  partial 
conformity;  and  a  negative  answer  to  the  question  of  par- 
tial conformity  carries  with  it  a  negative  answer  to  the 
question  of  complete  conformity.  These  two  rules  save 
much  labor  in  working  out  the  figures  in  the  table. 

Our  next  task  is  to  illustrate  the  eight  tests  by  applying 
them  to  a  particular  formula  for  Pi  and  the  correlative 
formula  for  Ti.     We  select  for  this  illustration  the  pair  of 

formulae  numbered    (11)    in  the  table,   namely  Pi  =  ^^ 

2poQi 

and  Ti  =  SpoQi,  and  we  seek  to  know  how  far  this  pair  of 

formulae  conform  to  the  eight  tests. 

Test  1.  Proportionality  as  to  prices.  — We  shall  begin  with 
"  the  particular  case  "  where  one  of  the  two  years  compared 
is  the  base  year.  In  concrete  terms,  this  test  means  that, 
if  all  prices  for  the  year  1  are  any  given  number  of  times 
(k  times)  the  prices  for  the  base  year  0,  then  the  index  num- 
ber for  the  year  1  (in  terms  of  the  year  0)  should  be  the 
same  number  k. 

The  test  is  best  expressed  in  algebraic  language  as  follows :  — 

If  ^=p;i=^=...  =fc, 

Po      Po      P  0 
i.e.  if  pi  =  kpQ ;  p\  =  kp'o ;  p'\  =  kp"o  •  •  •,  fc  being 

the  given  constant  price  ratio,  then  also  should 


410  THE    PURCHASING   POWER   OF   MONEY      [APPEND.  X 

Po      *' 

that  is  (since  Po  =  1),  Pi  =  k. 

It  is  easy  to  apply  this  test  to  our  given  pair  of  formulae. 

The  formulae  for  year  1  are  Pi  =  §^' ;  Ti  =  SpoQi- 

The  formulae  for  year  0  are     Po  =  |^  ( =  1) ;   To  =  ^poQo. 

^PoQo 

It  is  evident  that         Px  =  ^^  =  PiQ.^P^Q'^'h- 

^(kpo)Qi-\-(kp'o)Q\-\-  -_k(poQi  +  p'oQ\-\-  -") 
SpoQi  ^PoQi 

SpoQi 

Therefore  test  1  is  fulfilled  for  the  particular  case  when 
one  of  the  years  is  the  base  year. 

But,  as  we  have  noted,  it  does  not  follow  that  the  test  is 
fulfilled  in  general.  For  "  the  general  case "  of  any  two 
years  the  test  may  be  thus  stated :  If  the  price  of  each  good 
for  the  year  1  is  /c  times  the  price  of  the  same  good  for  the 
year  2,  then  the  index  number  for  the  year  1  (in  terms  of 
the  year  0)  should  also  be  k  times  the  index  number  for  the 
year  2  (in  terms  of  the  year  0).  That  this  may  be  true, 
the  test  requires,  for  the  general  case,  that  if 

Pi-2j-£li-  ...  -k 
-—    , 77 —         —  «'> 

P2        P2        P    2 

i.e.  if  pi  =  kp2,  p\  =  kp'2,  p"\  =  kp"z  etc., 

then  must  -^  =  k. 

P2 

This  general  test,  however,  will  not  be  fulfilled,  as  may  be 

seen  from  the  following :  — 

SpiQi     k%PiQx 

Pi  ^  SpoQi  ^  SpoQi  _ 

P2     SP2Q2      SP2Q2 

2poQ2      2poQ2 


Sec.  6]  APPENDIX  TO   CHAPTER  X  411 

In  order  that  this  last  expression  should  reduce  to  k,  it 
is  evident  that  l^E^i  would  have  to  be  equal  to  ^^-     But 

this  cannot  be  assumed  to  be  always  true.  If  this  equality 
should  happen  to  hold  true  for  any  particular  value  of  (say) 
Q2,  it  would  evidently  be  disturbed  by  the  slightest  deviation 
from  that  value.     If,  for  instance,  Q2  should  vary,  the  left 

side,  -£?^,  of  the  supposed  equality  would  be  unaffected,  but 

the  first  term  in  the  numerator  and  the  first  term  in  the 
denominator  of  the  right  side  would  vary.     Consequently  the 

right  fraction  -^^  would  be  affected,  except  when  the  ratio 

of  the  first  term,  ^^",  happened  to  be  equal  to  :~^,  in 
P0Q2  ^PoQz 

which  case  by  a  well-known  principle  of  proportion  (the 
principle  of  "composition  and  division")  the  size  of  the 
terms  P2Q2  and  P0Q2  would  be  immaterial. 

The  first  test,  therefore,  is  fulfilled  for  the  particular  case 
where  one  of  the  two  years  compared  is  the  base  year,  but  is 
not  fulfilled  in  general.  Therefore,  following  our  convention, 
we  assign  to  formula  11  the  number  ^  as  representing  its 
degree  of  conformity  to  test  2. 

Test  2.  Proportionality  as  to  trade.  This  test,  stated  for 
the  general  case,  is:  If  the  quantities  of  all  goods  sold  in  the 
year  1  is  fc  times  the  quantities  of  the  corresponding  goods 
sold  in  the  year  2,  the  index  number  of  trade  for  the  year 
1  (in  terms  of  the  year  0)  should  also  be  k  times  the  index 
number  for  the  year  2  (  n  terms  of  the  year  0). 

That  is,  if  Ql  =  Qj^  =  Ql!l=  ...  =h 

Q2     Q'2     Q'\ 

then  should  ~=  k. 


T. 


We  shall  find  that  this  test  is  fulfilled  in  the  general  case, 
and  therefore  also  in  the  particular  case. 


412  THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

Evidently  ?j  =  |2oQi  ^  h%p,Q,  ^  ^^ 

which  was  to  have  been  proved.  Therefore  test  2  is  com- 
pletely fulfilled,  and  the  formula  is  therefore  assigned  the 
full  credit,  "  1,"  in  the  table. 

Test  3.  Determinateness  as  to  prices.  This  test  is  also 
completely  fulfilled. 

If,  in  the  formula  for  Pi,  namely  —^^ ,  some  but  not  all 

^poQi 
of  the  prices,  as  pi,  or  one  of  the  quantities,  as  Qi,  should 
become  zero,  it  is  clear  that  the  above  expression  would  still 
be  determinate,  and  lie  between  zero  and  infinity.  It  will 
merely  happen  that  some  of  the  numerous  terms  in  the 
numerator  will  vanish,  but  all  the  other  terms  will  remain. 

P 

j    Since  the  same  reasoning  applies  to  P2.  it  follows  that  ^ 

must  also  be  de'^erminate,  being  the  quotient  of  two  finite, 
non-zero,  and  determinate  numbers.  Thus  test  3  is  com- 
pletely fulfilled. 

Test  4.  Determinateness  as  to  trade.  The  fourth  test  is 
analogous  to  the  third,  and  states  that  the  trade  index  num- 
ber must  not  be  rendered  indeterminate,  zero,  or  infinity 
simply  because   some   price  or   prices  should   become  zero. 

The  formula  for  Ti  is  always  -~^  •     Since,  as  neither  the 

-Pi 
numerator  nor  the   denominator   of  this   fraction  becomes 

zero,  infinity,  or  indeterminate  by  the  vanishing  of  some  but 
not  all  of  the  p's  or  Q's,  the  quotient  must  Ukewise  be  non- 
zero, finite,  and  determinate.  Thus,  test  4  is  completely 
fulfilled.^ 

^  It  might  seem  that  the  simple  tests  of  determinateness  "would  be 
fulfilled  by  any  formula  whatever,  but  such  is  not  the  case.  (If  it 
were,  the  total  "  score  "  given  in  the  last  column  opposite  test  4 
would  be  44  instead  of  31.)  Thus  the  simple  geometrical  average 
(formula  7)  will  not  conform  to  test  3  of  determinateness  as  to 
prices.     The  simple  geometrical  average  for  "n"  commodities  is 

Pi  =^21  .  2J^  ....    Evidently  if  pi  becomes  0,  the  value  of  the  entire 

^  po     p'o 


Sec.  G]  appendix  to  chapter  x  413 

Test  5.  Withdrawal  or  entry  as  to  prices.  Suppose  that 
there  are  100  specified  commodities.  If  the  general  price 
level  of  one  year  s  k  times  that  of  another,  and  if  any  good, 
the  price  of  which  in  the  one  year  is  k  times  that  in  the 
other,  be  withdrawn  from  the  100  commodities,  leaving  99, 
then  the  ratio  of  the  price  levels  of  the  two  years  should 
remain  unchanged. 

This  is  a  difficult  test  to  meet,  and  the  formula  under  dis- 
cussion meets  it  only  partially,  that  is,  when  one  of  the  two 
years  compared  is  the  base  year. 

If  J^^T^  =  ^}  where  A;  is  a  given  ratio, 

^PoQi 

and  if  also  ^  =  k,  then  we  are 

Po 

to  prove  that  J^  ri^  =  k,  where 
2p  oQ  1 

of  course  ^v'lQ'r  =  v'lQ'i  +  v"iQ'\  +  •  •• 

while  SpiQi  =  viQi  +  p'lQ'i  +  v"iQ"i +•  •• : 

so  that  Sp'iQ'i  =  SpiQi  —  piQx. 

Now  we  know  that, 

since  ^  =  fc, 

then  2i^^  =  /b.l 

And,  since  J^^T^  =  ^,  -t  follows  by  the  principle  of  pro- 

expression  becomes  0.  If,  therefore,  we  should  depend  on  the  geo- 
metric mean  for  ascertaining  price  levels,  the  temporary  plethora  of 
any  commodity,  to  the  extent  of  making  its  price  vanish  for  a  single 
moment,  would  cause  the  index  number  representing  the  entire  price 
level  for  that  moment  to  fall  to  0.  A  form  of  average  which  in  an 
extreme  case  is  so  absurd  will  approach  absurdity  before  the  ex- 
treme is  reached.  Thus  the  geometrical  average  is  unduly  affected 
by  prices  which  are  low,  even  if  not  actually  zero. 


414         THE   PURCHASING   POWER  OP  MONEY      [Append.  X 
portion  ("  composition  and  division  ")  that 

SpoQi  -  PoQi 
that  is,  J^ /a}  —  ^,  which  was  to  have  been  proved. 

If  the  missing  commodity  is  reentered,  the  ratio  will 
evidently  be  undisturbed,  so  the  rule  works  both  ways,  i.e. 
for  entry  as  well  as  for  withdrawal.  Therefore,  test  five  is 
fulfilled  for  the  particular  case. 

When,  however,  we  consider  the  general  case  for  price 
ratios  of  two  years  neither  of  which  is  the  base  year,  the  test 
will  not  be  fulfilled. 

That  is,  if       ^  =  k, 

^PoQ2 

and  if  also  —  =  k, 

Pi 


^P\Q' 


then  ^^°^/     will  not  in  general  be  equal  to  fc. 

^P  2V  2 


Sp'oQ' 


For,  if  this  expression  should  happen  to  be  equal  to  k  in  any 
particular  instance,  a  slight  change  in  any  base  year  price, 
such  as  p'q,  would  disturb  the  equality,  unless  the  variation 
in  p'o  should  affect  the  denominators  of  both  numerator  and 
denominator  of  the  last  expression  in  the  same  proportion. 

This  would  mean  that  the  ratio  J:  fii}  would  be  unaffected 

by  a  change  in  p'o,  which  in  turn  would  assume  (by  the  prin- 
ciple of  "  composition  and  division  ")  that 

p'oQ'2     2p'oQ'2* 


Sec.  6]  APPENDIX  TO   CHAPTER  X  415 

This  is  not  necessarily  true,  as  it  is  evidently  easy  to  assume 
values  for  (say)  Q'l  which  would  render  it  untrue.  Thus,  a 
doubling  of  Q\  would  double  the  left  side  but  not  the  right. 
Therefore  test  five  is  only  partially  met  by  our  formula. 
This  is  therefore  to  be  credited  only  with  ^  as  its  degree  of 
conformity  to  test  5. 

Test  6.  Withdrawal  or  entry  as  to  trade.  If  the  index 
numbers  for  trade  are  in  a  given  ratio,  the  inclusion  or  ex- 
clusion of  a  given  good,  the  quantities  of  which  are  in  the 
same  ratio,  ought  not  to  disturb  that  ratio.  This  test  is 
completely  fulfilled  by  our  formula. 

The  test  requires  that  if        ^  =  k, 
and  if  Tl  =  ^=.k, 

then  should  |2!o^i  =  fc. 

This  test  is  fulfilled;  for  from 

it  follows  that  ^oSl  =  fc^ 


PoQ; 


which  combined  with  J^^T^  =  ^> 

2poQ2 

by  the  principles  of  proportion  (i.e.  by  "composition  and 
division  ")  gives         ^PoQi-poQi  ^  j^ 

^PoQ2  —  P0Q2 

That  is,  ¥^  =  ^' 

W0Q2 

which  was  to  have  been  proved. 

Test  7.  Changing  the  base.  This  test  7  is  not  fulfilled 
by  our  formula  even  in  the  particular  case.  The  particular 
case  means  here  the  case  of  reversing  the  base,  as  between 
(say)  year  1  and  year  0. 


416         THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

In  order  not  to  alter  and  thereby  confuse  the  notation 
we  shall  have  to  use  the  subscript  0,  which  indicated 
the  original  base  year,  to  indicate  that  same  year,  even 
when,  for  the  moment,  it  is  not  considered  as  the  base 
year;  and  likewise  we  shall  use  the  subscript  1  to  indicate 
the  year  1,  even  when  it  is,  for  the  moment,  taken  as  the 
base  year. 

By  the  formula  which  we  are  testing,  the  price  index  ratio 

for  year  1  compared  to  year  0  as  the  base  is  ~~^-  By 
analogy  it  is  clear  that  the  price  index  ratio  for  year  0,  com- 
pared with  year  1  considered  as  the  base,  is  -^^  •     If  these 

two  expressions   are  reciprocals  of  each  other,  then  -r^ 

^PoQi 

should  be  equal  to  ;~~' 
^PoQo 

That  this  is  not  necessarily  true  is  evident,  since  there  is 
no  necessary  relation  between  the  Qo's  and  the  Qi's.  If  the 
equation  should  accidentally  hold  true  for  a  particular  set  of 
Qo's  and  Qi's,  the  change,  even  in  the  smallest  degree,  of  a 
single  letter,  say  Qo  or  Qi,  would  evidently  disturb  the  rela- 
tion. Therefore  the  test  is  not  fulfilled  even  for  the  par- 
ticular case  of  reversing  the  base  as  between  two  years,  and 
the  formula  must  therefore  be  assigned  a  "0"  or  complete 
failure  to  conform  to  test  7. 

Test  8.  Changing  units  of  measurement.  If  the  unit  for 
indicating  the  price,  say  of  coal,  should  be  changed  from 
a  ton  to  a  pound,  the  index  number  ought  not  to  be 
affected  thereby.  We  shall  find  that  this  test  is  met  by 
formula  (11). 

Evidently  a  change  of  unit,  say  from  a  ton  to  a  pound, 
applied  to  any  particular  goods  (the  prices  of  which  are 
Ph  P'h  P"h  the  corresponding  quantities  being  Qi,  Q'l,  Q"i) 
will  magnify  all  the  Q's  2000  times,  but,  on  the  other  hand, 
will  reduce  all  the  p's  in  the  reciprocal  ratio  (tttW)-  Con- 
sequently, the  products  piQ\,  p'xQ'i,  p"\Q"\,  will  be  unaffected. 


Sec.  6]  APPENDIX   TO    CHAPTER   X  417 

Hence  the  sum  of  such  products  constituting  the  numerator 
and  denominator  of  the  right  side  of  the  equation 

Pi  _  ^PoQi 

Pz      SP2Q2 

will  likewise  be  unaffected.     Therefore  the  ratio  of  the  index 

p 
numbers  — ^  will  be  unaffected.     Hence  the  test  is  completely 

P2 

fulfilled.* 

^  It  might  seem  that  every  index  number  would  conform  to  this 
unit-shifting  test.  It  is  true  of  40  formulae  out  of  the  44.  Yet  the 
index  number  which  is  perhaps  the   simplest  of  all,  Bradstreet's, 

Pi  =  ~^ ,  fails  to  conform. 

It  is  evident  that  if  there  is  a  change  in  the  unit  of  any  one  com- 
modity, such  as  that  whose  prices  are  pi,  and  po,  both  the  numerator 
and  denominator  will  be  affected,  but  not  in  the  same  proportion, 
except  when  it  happens  that 

pi_  Spi 
po     Spo* 

Consequently,  the  index  number  is  dependent  upon  the  nnitof 
measurement.  Such  an  index  number  is  entirely  arbitrary,  and  by 
sufficient  manipulation  of  the  units  of  measurement  could  be  made 
to  favor  any  particular  commodity.  The  larger  the  unit  of  any 
particular  commodity  employed,  the  higher  the  price  for  it  which 
enters  into  the  formula,  and  the  more  that  commodity  tends  to 
affect  the  result. 

Bradstreet  uses  96  commodities  in  common  use,  all  of  which  are 
measured  by  the  pound.  The  result  is  that  silver,  for  instance, 
dominates  over  iron,  entering  at  several  dollars  a  pound  instead  of 
a  few  cents.  If  radium,  which  recently  cost  $8,000,000  an  ounce,  were 
included,  it  would  absolutely  dominate  the  group,  and  we  would 
reach  the  absurd  result  that  since  radium  has  fallen  to  hundreds  of 
thousands  instead  of  millions  of  dollars  an  ounce,  the  general  price 
level  must  have  fallen  several  fold  in  spite  of  the  general  impression 
of  rising  prices !  An  index  number  of  this  kind  is  fitly  called  by 
Walsh  one  of  accidental  or  haphazard  weighting. 


2k 


418         THE   PURCHASING   POWER   OF  MONEY      [Append.  X 

§  7.   The  44  Formulce  Compared 
We  have  gone  through  the  reasoning  by  which  the  con- 
formity of  one  pair   (Pi  =  ^^ ;    Ti  =  SpoQi)  out  of  the 

44  pairs  of  index  numbers  of  prices  and  trade,  given  in  the 
table,  are  tested  and  graded  with  respect  to  the  eight  tests. 
The  table  contains  for  the  remaining  43  formulae  the  results 
of  similar  reasoning.  This  reasoning  is  here  omitted  to  save 
space.  The  mathematical  reader  who  chooses  can  verify  the 
results  as  tabulated.  He  can  also  prove  the  relationship  by 
which  it  follows  that  the  figure  in  any  column  for  the  odd 
tests  corresponds  to  that  in  the  neighboring  antithetical  col- 
umn for  the  even  tests.  In  consequence  of  this  relationship 
the  sum  of  any  column  for  the  odd  tests  equals  the  sum  in 
the  antithetical  column  for  the  even  tests.  In  fact,  the  table 
is  full  of  correspondences  and  relationships  of  many  kinds. 

The  footings  give  us  a  means  of  comparing  the  merits  of 
the  various  index  numbers.  These  footings  are  intended  to 
express,  so  far  as  may  be,  the  fitness  of  the  formulas  to  serve 
as  index  numbers  for  price  levels.  Consequently  the  score 
for  test  6  should  be  omitted  from  the  footing,  as  test  6  has 
no  value  in  regard  to  'prices.  (If  it  be  desired  to  compare  the 
scores  of  the  correlative  index  numbers  for  quantities  or 
trade,  the  score  of  test  6  will  be  included,  but  that  of  test  5 
should  then  be  omitted.) 

Thus  a  perfect  score  would  be  seven.  The  highest  score  in 
the  table  is  5^,  the  lowest,  2. 

It  would,  of  course,  be  absurd  to  compare  the  merits  of 
index  numbers  merely  by  their  "score"  in  the  table.  This 
score  is  more  or  less  arbitrary,  and  it  treats  all  seven  tests  as 
equally  important.  Yet  it  affords  at  least  some  insight  into 
the  comparative  characteristics  of  the  44  formulae.  It  is 
noteworthy  that,  in  general,  the  simplest  formulae  have  high 
scores  and  the  most  compUcated  have  low  scores.  Thus 
formulae  1  (Dutot),  7  (simple  geometric),  9  (median),  11  and 
12  (Scrope)  have  scores  of  5  and  5^.    The  only  others  as 


^(80t 

(31) 

" 

TU./ 

1    AC 

0 

i  ■ 

1 

0 

1 

1 

0 

1 

0 

1 

(1) 

(0) 

0 

0 

1 

1 

3 

3 

• 

m 

( 

I 

\ 

1 

1 

jss. 

^ 

■■5 

f 

■^ 

"■?■ 

"'■        #• 

.._. — ~.                1 

,..«_ — 

,-4 ...^ 

■",' 

i 

:J~- 1 

,       1       ,             , 
1 

.1        1        s                »' 

L    t 

s 

■KSf  1    ... 

m 

m 

jftl-«a'>" 

ss 

'■^ 

'■^ 

r^ 

as 

— ip 

■tISs 

* 

■"*!■        ^           >         ^£,--- •"■•<'::' - 

— 

--"-'" 

,^ 

•niT)- 

..4^.. 

-*— -, 

' 

,  1  ., 

~ 

.r  ,  1  ,                        i'w,  " 

1    ;    . 

) 

1 

„      ,   i  „  I  .  1  „ 

1  T 

. 

B 

»  ,   >      

« 

1 

II      ,      I      j      « 

,        1          0          1           ,                     0 

» 

'  1  "    '    '  i'  '    ' 

.     . 

1     ll      1      1      1    1    1 

■ 

,_„. 

,      1     0     1    ,■       oil, 

• 

0 

° 

i           »           ,      1      »     1    1    1    0     ■     1       1       0 

1 

" 

» 

101 

(0) 

m        111 

' 

^°_ 

•i- — 

Z^^i^::_^_,, 

~ 

i~ 

4^ 

7l" 

'    1    ' 

1            1            1 

fJSi^'J^  ~~  —  ■ ' " 

4 

1    1    1 

J            n 

'^^^^^~f. 

• 

( 

»                        c 

o 

Sec.  7] 


APPENDIX   TO   CHAPTER   X 


419 


high  as  5  are  "mixtures"  of  formulae  11  and  12.  The  simple 
arithmetical  (3)  and  simple  harmonic  (5)  have  a  score  of  4, 
which  is  fairly  high.  The  more  comphcated  forms  which 
have  fairly  high  scores  are  in  several  cases  "mixtures," 
averages,  or  antitheses  of  simple  formulae  11  and  12. 

The  above  comparisons  treat  all  the  other  seven  tests  as 
of  equal  importance.  But  they  are  not  of  equal  importance. 
Since  opinions  might  differ  as  to  the  exact  relative  impor- 
tance of  the  various  tests,  we  shall  not  attempt  to  "weight" 
them.  Nor  will  this  be  necessary  in  order  to  decide  the 
question  of  most  importance  to  us,  viz.,  which  of  the  44 
index  numbers  meet  the  tests  most  completely.  Tests  3  and 
4  are  probably  of  little  practical  importance  as  compared 
with  the  remaining  tests.  Test  2,  on  the  other  hand,  may  be 
accorded  chief  importance,  for  reasons  given  in  section  5  of 
this  Appendix  and  in  Chapter  II.  In  order  to  select  the 
best  index  numbers  of  prices,  therefore,  let  us  first  rule  out 
of  the  competition  all  the  18  formulae  which  have  "0"  for 
test  2.  We  have  left  the  following  formulae  classified  into 
two  groups. 

(Omitting  test  6),  score  for  formulae  which  do  not  com- 
pletely fail  on  test  2, 


Formula  completely  fulfilling 

Test  2 

Formula  partially  fulfilling  iest  z 

Formulae 

Score 

Formulse 

Score 

2 

4 

12 

5i 

4 

3 

13 

4 

6 

3 

14 

4 

8 

4 

15 

4i 

10 

H 

16 

^l 

11 

5 

17 

5 

28 

4 

18 

H 

30 

3 

20 

4 

34 

3 

21 

5 

38 

3 

22 

4i 

24 

4 

26 

3i 

32 

2i 

36 

2i 

42 

2* 

420 


THE    PURCHASING    POWER   OF  MONEY      [Append.  X 


If,  next,  we  rule  out  of  the  competition  from  among  those 
which  completely  meet  test  2,  all  except  those  which  have 
scores  of  4J  or  above,  we  have  left  only  formulae  num- 
bers 10  and  11.  Among  the  formulae  which  only  partially 
meet  test  2  we  may  eliminate  all  which  fail  to  exceed  4^  in 
total  score ;  for,  although  those  which  reach  4^  tie  formula 
10,  yet  when  all  tests  are  counted  as  of  equal  importance, 
they  are  inferior  in  not  completely  meeting  the  most  impor- 
tant test  —  test  2.  Putting  the  matter  in  another  way,  we 
may  say  that  if  test  2  should  be  weighted  more  heavily  than 
the  other  tests,  the  scores  of  those  formulae  half  meeting  that 
test  which  now  tie  formulae  wholly  meeting  that  test  would 
fail  to  do  so  and  would  therefore  drop  out  of  competition 
with  formulae  10  and  11  in  the  first  column. 

Eliminating  therefore  from  the  second  column  all  formulae 
with  scores  of  4^  or  less,  we  have  as  the  only  rivals  of  formulae 
10  and  11,  formulae  12,  17,  and  21,  having  scores  of  5|,  5,  and 
5  respectively.  Our  best  formula,  therefore,  should  be  found 
among  numbers  10,  11,  12,  17,  21.  We  shall  therefore  exam- 
ine with  particular  care  these  five  surviving  competitors. 

These  all  conform  to  tests  3,  4,  and  8.  Comparing  them 
in  other  respects,  we  find :  — 


10 

11 

12 

17 

21 

Test  1 

Test  2 

Test  5 

Test  7 

0 

1 
0 

i 

1 

i 

0 

1 

1 
0 

i 
1 

i 

Total 

U 

2 

2i 

2 

2 

Tests  17  and  21  have  scores  identical  in  every  instance,  and 
may  therefore  be  said  to  be  tied. 

Comparing  tests  11  with  17  (or  21),  we  see  that  11  excels 
in  respect  to  the  important  test  2,  and  17  in  test  7.  As  test 
2  is  regarded  as  of  more   importance  than  test  7,  we  may 


Sec.  7]  APPENDIX  TO   CHAPTER   X  421 

safely  give  the  preference  to  formula  11  over  17  (or  21). 
We  therefore  now  strike  out  17  and  21  from  the  competition. 

We  have  left  formulae  10,  11,  12;  comparing  10  and  11,  we 
note  that  10  excels  in  test  7,  while  11  excels  in  tests  1  and  5. 
If  we  maybe  allowed  here  to  exercise  a  comparative  judgment, 
we  shall  say  that  the  superiority  in  the  one  test  7  is  more  than 
offset  by  superiority  in  the  two  tests,  1  and  5.  We  therefore 
eliminate  formula  10. 

We  now  have  left  only  the  two  formulae,  11  and  12.  There 
is  not  much  to  choose  between  them.  While  12  has  the  higher 
score  when  all  tests  are  counted  as  of  equal  importance,  11 
excels  in  the  most  important  test  2,  and  we  are  therefore  in- 
clined to  give  it  the  preference. 

According  to  our  judgment,  therefore,  test  11  emerges  as 
the  winner  in  the  score  contest.  It  has  also  the  advantage 
of  being  among  the  very  simplest  formulae  and  of  having  as 
its  correlative  formula  for  T  the  simplest  of  all  formulae  for  T, 
viz.  Ti  =  :SpoQi. 

In  nonmathematical  language,  the  pair  of  formulae  11 
mean  that  the  level  of  prices  in  any  year  is  found  by  dividing 
the  total  value  of  the  quantities  sold  in  that  tjear  by  what  that 
value  would  have  been  at  base  prices,  and  that  the  trade  index 
in  any  year  is  simply  the  value  of  the  quantities  sold  in  that 
year  reckoned  at  base  prices. 

Applying  formula  11  to  the   equation   of  exchange,  we 

have  — 

MV  +  M'V  =  ^PiQi  (1) 

=  PiTi  (2) 


Kipt)^^*^'         ''' 


We  wish  now  to  emphasize  once  more  the  virtues  of  this 
formula  11  in  respect  to  test  2.  The  equation  of  exchange, 
stated  above,  is  intended  to  show  how  prices  are  affected  by 
changes  in  M,  M',  V,  V  or  the  Q's.  It  is  evident  from  the 
original  form  (1)  of  this  equation  that  a  proportional  chane:e 
in  the  M  and  M'  (if  the  V's  and  Q's  remain  unchanged)  will 


422  THE    PURCHASING   POWER   OF   MONET      IAppend.  X 

affect  all  the  pi's  in  exactly  the  same  ratio,  or  else  raise  some 
prices  more  and  others  enough  less  than  this  ratio  to  com- 
pensate in  the  sense  that  the  equation  of  exchange  will  be 
preserved.  In  some  sense,  therefore,  the  general  level  of  prices 
varies  exactly  with  M  and  M'.  Form  (3)  enables  us  to  ex- 
press this  proportionality  by  formulating  the  price  level  as 

the  fraction  ^^M.     xhig  varies  directly  with  the  M's. 
SpoQi 

In  precisely  the  same  way  we  are  enabled  to  state  that  a 

uniform  change  in  the  two  V's,  or  any  change  in  the  left  side 

of  the  equation  as  a  whole,  will  affect  prices  in  precisely  the 

same  ratio  (the  QiS  being  assmned  constant).     We  may  also 

say  that  a  uniform  change  in  the  Qi's  will  affect  Ti  in  exactly 

the  same  ratio,  and  Pi  in  exactly  the  inverse  ratio  (assuming 

the  left  side  of  the  equation  to  be  unchanged).     In  fact,  if 

we  use  formula  11  to  express  the  average  price  ratio,  we  are 

able  to  state  in  all  cases  (so  long  only  as  the  Qi's  change  in 

unison  or  not  at  all)  that  prices  rise  or  fall  "on  the  average" 

directly  as  the  left  side  of  the  equation,  and  inversely  as  the 

Qi's. 

As  noted,  these  are  the  basic  theorems  for  which  the  equa- 
tion of  exchange  stands.  We  would  naturally  like  to  remove 
the  restriction  as  to  the  Qi's  changing  uniformly.  We  should 
consider  an  index  number  perfect  (so  far  as  needed  in  the 
equation  of  exchange)  if  we  could  assert  of  it  the  same 
theorem  of  proportion  as  above,  without  the  restriction  as  to 
the  Qi's  changing  uniformly,  so  that  we  might  substitute  an 
average  change  in  the  Q's  in  place  of  a  uniform  change.  No 
such  index  is  found  in  the  table,  and  no  such  index  seems 
possible.  Practically  this  conclusion  does  not  greatly  mat- 
ter, for  we  are  interested  in  prices  far  more  than  in  quantities, 
the  latter  being  chiefly  important  as  supplying  weights  for 
the  price  indexes.  As  we  have  already  noted,  Edgewortb 
has  shown  that  considerable  variation  in  weighting  is  ol 
comparatively  little  practical  importance. 

The  chief  use  of  index  numbers  is  to  compare  succesdvi^ 
years,  not  years  remotely  distant  from  each  other.    We  ar^ 


Sec.  7]  APPENDIX  TO   CHAPTER   X  423 

not  so  much  interested  in  comparing  the  prices  of  1909  and 
1910  each  with  those  of  1873  as  we  are  in  comparing  them  with 
each  other.  In  fact,  the  chief  use  of  1873  as  a  base  year  is  to 
enable  us  to  compare  any  other  two  years  with  each  other. 
But  only  a  few  index  numbers  which  afford  a  true  comparison 
between  any  year  and  another  year  as  the  base  will  give  a 
true  comparison  between  any  two  years,  each  in  terms  of  a 
third  year  as  the  base.  These  few  index  numbers  are  those 
which  completely  meet  the  base-shifting  test  7.^  In  the  table 
the  only  formulae  which  come  up  to  this  requirement  are  for- 
mulae numbered  1,  2,  7,  8,  43,  44,  to  all  of  which  there  are 
serious  objections  on  other  grounds.  Formulae  1  and  2  are 
very  arbitrary,  having  "haphazard  weighting";  formulae  43 
and  44  have  the  lowest  scores  in  the  table ;  formula  7  has  no 
system  of  weighting;  and  formula  8  becomes  zero  if  a  single 
quantity,  as  Q,  should  disappear  from  a  year's  sales. 

The  question  therefore  arises,  why  should  we,  as  has  usually 
been  done,  construct  our  index  numbers  with  reference  to  a 
fixed  base  in  terms  of  which  we  indirectly  compare  two  given 
years?  Why  not  make  the  comparison  directly f  The  in- 
direct comparison  introduces  an  error  in  all  cases  except  of 
those  formulae  which  conform  to  test  7.  In  these  cases  the 
indirect  comparison  cannot,  of  course,  give  any  better  result 
than  the  direct  comparison,  while  in  all  other  cases  the  direct 
comparison  is  better. 

It  seems,  therefore,  advisable  to  compare  each  year  with 
the  next,  or,  in  other  words,  to  make  each  year  the  base  year 
for  the  next.  Such  a  procedure  has  been  recommended  by 
Marshall,  Edgeworth,  and  Flux.^     It  largely  meets  the  diffi- 

^  That  this  test  is  the  most  difficult  one  to  meet  is  shown  by  the 
fact  that  the  total  "  score  "  as  given  in  the  last  column  opposite  test 
7  is  the  lowest  in  that  column,  being  only  12  out  of  a  possible  44; 
the  next  most  difficult  test  to  meet  is  test  5  (or  6),  opposite  which 
the  total  "  score  "  is  13j. 

The  easiest  test  to  meet  is  test  8,  opposite  which  the  total  is  40 
out  of  44  ;  the  next  easiest  is  test  3  (and  4)  with  31  out  of  44. 

* "  Modes  of  constructing  Index  Numbers,'!  Quarterly  Journal  oj 
Economics,  August,  1907,  pp.  613-631. 


424  THE    PURCHASING   POWER  OF  MONEY      [Append.  X 

culty  of  non-uniform  changes  in  the  Q's,  for  any  inequalities 
for  successive  years  are  relatively  small. 

Such  successive  index  numbers,  each  on  the  basis  of  100 
per  cent  for  the  previous  year,  will,  if  multiplied  together, 
give  a  chain  of  index  numbers  showing  the  fluctuations  from 
year  to  year,  like  any  ordinary  series,  but  much  more  suitable 
for  comparison  of  neighboring  years. 

Let  us  now  reexamine  the  comparative  merits  of  index 
numbers  on  the  supposition  that  they  are  to  be  used  only  for 
successive  years,  that  is,  for  comparison  between  each  year 
and  the  previous  year  as  a  base.  In  this  case  we  do  not  need 
to  distinguish  between  a  "partial"  and  a  "complete"  ful- 
fillment of  the  tests.  We  may  therefore  now  substitute  "  1 " 
for  every  "^."  Omitting,  as  before,  all  formulae  which  fail 
to  meet  test  2,  we  have  the  following  results  :  — 


Formula 

Score 

Formula 

Score 

2 

4 

20 

5 

4 

3 

21 

7 

6 

3 

22 

6 

8 

4 

24 

5 

10 

4i 

26 

4 

11 

6 

28 

4 

12 

6 

30 

3 

13 

5 

32 

3 

14 

5 

34 

3 

15 

6 

36 

3 

16 

6 

38 

3 

17 

7 

40 

3 

18 

6 

42 

3 

19 

6 

We  note  that  formulae  11  and  12  have  scores  of  6  each,  while 
their  average  15  (and  16)  and  their  mixture  18  and  also  22 
have  the  same  score,  but  that  formulae  17  and  21,  which  are 
mixtures  of  11  and  12,  have  perfect  scores,  7.  Each  of  these 
two  formulae  uses  as  weights  the  average  of  the  weights  used 
in  formulae  11  and  12.  Theoretically,  therefore,  we  find  two 
formulae  which  fit  all  tests  perfectly  so  far  as  year-to-year 
comparisons  of  prices  are  concerned. 


Sec.  8]  APPENDIX   TO   CHAPTER   X  425 

Where,  therefore,  great  accuracy  is  desired  and  there  exist 
abundant  funds  to  provide  for  the  laborious  computations 
necessary,  we  may  recommend  the  use  of  formula  17  or  21, 
This  presupposes  that  statistics  are  available  for  the  Q's, 
which  is  not  usually  the  case. 

Thus  far  our  conclusions  therefore  are  (1)  that  theoretically 
formula  11  is  the  best  when  each  year  is  expressed  in  terms  of 
a  common  base;  (2)  that  (also  theoretically)  formulae  17  and 
21  are  slightly  superior  when  each  year  is  expressed  in  terms 
of  the  preceding  year  as  base,  and  that  these  two  meet  all 
tests  for  year-to-year  comparisons. 

§  8.   Reasons  for  preferring  the  Median  for  Practical  Purposes 

Practically,  however,  there  is  little  if  any  advantage  in  17 
and  21  over  11  (or  12,  which  in  the  case  of  year-to-year  com- 
parisons amounts  to  the  same  thing)  because  (1)  weighting 
is  of  little  importance ;  (2)  the  more  perfect  weighting  con- 
tained in  formulae  17  and  21  will  seldom  differ  materially 
from  that  of  11  and  12,  for  any  gain  of  precision  would  prob- 
ably be  less  than  the  errors  in  measurement  of  the  Q's,  which 
are  never  exactly  known ;  (3)  the  systems  of  17  and  21  are 
practically  far  more  laborious.  In  the  end  we  must  be  guided 
largely  by  practical  considerations  except  where  the  great 
labor  and  expense  of  computation  may  be  disregarded.  If 
in  a  practical  spirit  we  examine  the  merits  of  the  various 
formulae,  we  shall,  I  believe,  reject  all  formulae  except  9  and 
11,  and  come  to  the  conclusion  that  the  best  index  number  is 
the  weighted  median.  It  has  no  rival  in  ease  of  computation. 
The  score  of  the  median  in  the  table  (formula  9)  is  high, 
although  it  fails  in  test  2.  Excepting  this  test  it  meets, 
partially  or  wholly,  every  other  test.  It  therefore  possesses 
some  merit  even  on  the  theoretical  side. 

In  passing,  we  may  mention  a  feature  of  medians,  although 
I  am  disposed  to  regard  it  as  a  fault.  Edgeworth  empha- 
sized the  fact  that  price  dispersion  upward  always  or  usually 
exceeds  the  price  dispersion  downward.    There  is  no  limit  to 


426  THE    PURCHASING   POWER  OF  MONEY      [Append.  X 

the  former,  but  the  latter  is  limited  by  zero.  Statistical  tests 
show  clearly  this  asymmetry  of  dispersion.*  From  this  fact 
it  has  been  argued  that  the  best  average  should  be  one  from 
which  large  deviations  above  it  count  no  more  than  small 
deviations  below  it.  This  condition,  whether  good  or  ill, 
is  not  met  by  arithmetical  averages,  but  is  met  by  the  geo- 
metric average  and  by  the  median  ^  which,  in  fact,  usu- 
ally closely  follows  the  geometric  average.  Edgeworth  also 
argues  that  the  median  is  superior  when  the  variabilities  of 
the  various  elements  averaged  are  widely  different.* 

Edgeworth  concludes  that  "in  the  present  state  of  our 
knowledge,  and  for  the  purposes  on  hand,  the  median  is  the 
proper  formula."  * 

As  to  methods  of  weighting,  theoretical  discussion  with 
reference  to  test  2  shows  that  the  weighting  should  be  made 
on  the  basis  of  values  sold  in  one  or  the  other  of  the  years 
compared. 

It  is  easy  to  show  that  a  system  of  weighting  the  median 
by  given  weights,  that  is,  by  counting  each  price  ratio,  not  only 

*  See  Edgeworth,  "First  Report  on  Monetary  Standard,"  Report 
of  the  British  Association  for  the  Advancement  of  Science,  1887,  pp. 
284-855. 

^  Edgeworth,  ibid.,  pp.  284-286.  From  the  standpoint,  however, 
of  the  relation  of  prices  to  the  currency,  a  large  upward  variation 
should  count  more  than  a  small  downward  variation  ;  for  it  requires 
more  currency.  In  fact,  as  we  have  already  seen,  the  arithmetical 
average  complained  of  is  precisely  the  average  needed  to  fit  into  the 
aquation  of  exchange.  See  §  6  of  Appendix  to  Chapter  II  and  §  7 
of  this  Appendix.  As  to  the  asymmetry  of  price  dispersion,  sea 
Mitchell,  Gold,  Prices,  and  Wages  under  the  Greenback  Standard} 
Berkeley  (University  of  California  Press),  1908,  and  reviews  of  same 
by  Edgeworth,  Journal  of  the  Royal  Economic  Society,  December, 
1908,  pp.  578-582  ;  and  H.  G.  Brown,  Yale  Review,  May,  1909, 
pp.  99-101. 

»  Edgeworth,  Report,  etc.,  1887,  p.  291,  and  "On  the  Choice  of 
Means,''  Philosophical  Magazine,  September,  1887;  see  also  Report 
of  the  British  Association  for  the  Advancement  of  Science,  1889,  pp. 
156-161,  and  Journal  of  the  Royal  Statistical  Society,  June,  1888. 

*  Ibid.,  p.  191. 


Sec.  8]  APPENDIX  TO   CHAPTER  X  427 

once  but  a  certain  number  of  times  (that  number  being  the 
weight)  will  not  affect  the  relative  fulfillments  of  the  tests  as 
met  by  the  simple  median  9,  which  is  the  only  median  in  the 
table.  Edgeworth  has  shown  that  for  all  practical  purposes 
a  very  rough  system  of  weighting  will  suffice.^  Whether  the 
weighting  be  according  to  the  values  PoQo,  etc.,  or  piQi,  etc., 
or  poQi,  etc.,  or  piQo,  etc.,  is  usually  of  no  practical  importance 
whatever.  If,  then,  we  subordinate  theoretical  to  practical 
considerations,  the  proper  procedure  would  seem  to  be  to 
select  certain  constants  consisting  of  simple  integers,  and  as 
near  as  may  be  to  the  values  dealt  with  in  the  years  consid- 
ered. These  weights  need  not  be  changed  every  year,  but 
should  be  changed  when  the  values  (piQi)  change  very  greatly. 

If  it  be  desired  to  have  a  quantity  or  trade-index  number 
(Qi,  or  Ti)  as  well  as  a  price-index  number  (Pi),  we  may  like- 
wise select  as  the  form  for  Qi  the  median.  In  other  words, 
the  indexes  for  p's  and  Q's  are  best  selected  independently  of 
each  other.  It  is  true  we  thereby  abandon  any  absolute  mu- 
tual consistency  between  the  two,  but  we  are  now  speaking 
of  practical,  not  theoretical,  considerations. 

One  of  the  great  practical  advantages  of  the  median  is  its 
use  in  conjunction  with  "quartiles"  or  "deciles"  to  portray 
dispersion  as  well  as  averages.  This  method  of  showing  dis- 
persion about  a  mean  is  both  easier  to  calculate,  and  capable 
of  more  detail,  if  detail  be  desired,  than  the  method  of  Karl 
Pearson  of  the  "Standard  Deviation"  about  an  arithmetical 
mean. 

The  final  practical  conclusion,  therefore,  is  that  the  weighted 
median  serves  the  purposes  of  a  practical  barometer  of  prices, 
and  also  of  quantities  as  well  as,  if  not  better  than,  formulae 
theoretically  superior. 

In  spite,  however,  of  the  peculiar  simplicity  and  ease  of 

*  See  Report  of  the  British  Association  for  the  Advancement  of 
Science,  1888,  pp.  208-211.  Edgeworth  compares  various  means 
for  21  articles  in  1885  and  1873,  one  being  that  recommended  by  the 
committee  of  which  he  was  a  member,  and  above  referred  to  in  the 
text  of  Chapter  X,  §  5. 


428  THE    PURCHASING   POWER   OF  MONEY      [Append.  X 

computation  which  characterizes  the  median,  and  in  spite  of 
Edgeworth's  strong  indorsement,  it  remains  still  almost 
totally  unused,  if  not  unknown.  Wesley  C.  Mitchell  ^  has 
used  the  median  for  price  indexes  more  extensively  than  any 
one  else.  Professor  Davis  R.  Dewey  has  used  them  for  wages 
in  his  special  Census  report  on  that  subject. 

§  9.  Summary 

The  conclusions  of  this  Appendix  may  be  briefly  stated  as 
follows :  — 

1.  Any  sum  of  products  of  two  factors  each,  such  as  SpQ, 
may  be  converted  into  any  one  of  three  forms :  (1)  PT,  in 
which  P  is  an  average  of  the  ratios  of  the  p's  to  some  base 

po's,  and  T  is  the  quotient  — w-  ;  (2)  AQ,  in  which  Q  is  an 
average  of  the  ratios  of  the  Q's  to  some  base  Qo's,  and  A  is  the 
quotient  -^  ;  (3)  PQSpoQo- 

2.  Of  the  foregoing  three  formulae  only  the  last  is  synmietri- 
cal  in  the  sense  that  the  p's  and  Q's  are  treated  alike. 

3.  P  and  T  (or  P  and  Q)  are  said  to  be  correlative,  and  any 
particular  formula  for  either  implies  a  particular  correlative 
formula  for  the  other. 

4.  Two  correlative  formulae  for  P  and  Q  are,  in  general, 
quite  unlike  each  other.  If  like  formulae  be  constructed  for 
P  and  Q,  the  correlate  of  Q  constitutes  a  new  formula  for  P, 

^  Gold,  Prices,  and  Wages  under  the  Greenback  Standard,  Publica- 
tions of  the  University  of  California.  Mitchell's  use  of  deciles, 
however,  is  of  small  value,  as  he  employs  a  common  base,  1860,  so 
that  his  figures  for  each  subsequent  year  give  the  dispersion  of  that 
year  relatively  to  1860.  There  is  practically  no  use  in  knowing  the 
dispersion  of  prices  in  1909  or  1910  as  compared  with  1860,  and  this 
knowledge  throws  no  light  on  whether  prices  change  uniformly  or 
disperse  widely  from  1909  to  1910.  What  is  needed  is  a  knowledge 
of  price  dispersion  from  year  to  year,  and  this  can  readily  be  in- 
dicated by  drawing  three  radiating  lines  from  1909  to  1910,  the 
central  one  to  show  the  movement  of  the  median,  and  the  other  two 
to  show  the  movements  of  the  two  neighboring  quartiles. 


Sec.  9]  APPENDIX  TO   CHAPTER   X  429 

said  to  be  antithetical  to  the  original  formula  for  P,  and 
vice  versa. 

5.  There  are  an  indefinite  number  of  formulae  for  P,  of 
which  44  are  given  in  the  table ;  and  there  are  at  least  8 
important  tests  to  which  each  formula  may  conform  in  one 
of  three  degrees  (1)  wholly,  or  for  the  ratio  of  Pi  to  P2,  each 
being  relative  to  a  third  year  as  a  base ;  (2)  partially,  or  for 
the  ratio  Pi  to  unity ;  and  (3)  not  at  all. 

6.  The  eight  tests  are  of  proportionality  as  to  prices  or 
quantities  (1  and  2) ;  deter minateness  as  to  prices  or  quan- 
tities (3  and  4) ;  withdrawal  or  entry  as  to  prices  and  quanti- 
ties (5  and  6) ;  changing  base  as  to  prices  and  quantities  (7) ; 
and  changing  units  as  to  prices  and  quantities  (8) . 

7.  The  tests  arrange  themselves  in  pairs,  one  of  each  pair 
relating  to  the  p's  in  the  same  manner  as  the  other  is  related 
to  the  Q's;  but  each  test  has  significance  both  with  respect 
to  the  p's  and  the  Q's. 

8.  The  formulae  arrange  themselves  in  antithetical  pairs. 

9.  Of  any  four  neighboring  compartments  in  the  table, 
relating  to  two  correlative  rows  (tests)  and  two  antithetical 
columns  (formulae),  the  diagonals  will  have  the  same  "scores." 

10.  No  known  form  of  index  number  P  conforms  perfectly 
to  all  the  eight  tests  when  a  common  base  year  is  employed, 

but  several  conform  well,  the  best  being  formula  No.  11,^^^^^' 

2poQi 

11.  But  if  we  are  content  with  year-to-year  comparisons, 
renouncing  comparisons  in  terms  of  a  third  year,  there  are 
two  formulae  which  conform  perfectly,  viz.  formulae  17  and  21. 

12.  Practically,  however,  formula  11  is  superior  to  17  or 
21,  and  formula  9  (median)  — when  properly  "weighted"  — 
is  superior  to  11. 

13.  For  practical  purposes,  therefore,  unless  the  expense  and 
labor  of  computation  can  be  disregarded,  the  median  (with 
its  two  neighboring  quartiles)  is  recommended,  with  a  simple 
system  of  weights  (whole  numbers)  based  on  expenditures, 
and  changing  from  time  to  time  for  the  sake  of  making  better 
year-to-year  comparisons. 


APPENDIX  TO  CHAPTER  XII 

§  1  (to  Chapter  XII,  §  1) 
Professor  Kemmerer's  Calculations 

Professor  Kemmerer  (Money  and  Prices,  p.  99)  estimates 
the  money  in  circulation  (M)  by  deducting  from  the  money 
in  the  United  States,  as  estimated  by  the  Comptroller  of  the 
Currency,  two  items,  viz.  the  money  in  the  United  States 
treasury  and  that  in  banks  (reported  and  estimated).  He 
then  estimates  the  velocity  of  circulation  of  money  as  47 
times  a  year,  and  assumes,  in  the  absence  of  any  data  by  which 
to  estimate  its  variations,  that  it  remains  constant.  He 
arrives  at  the  figure  47  as  follows :  The  amount  of  check 
transactions  he  first  estimates  for  1896,  at  143  billions  (p.  111). 
This  estimate  is  based  on  figures  taken  from  Kinley's  investi- 
gation, made  through  the  Comptroller  of  the  Currency  in 
1896.  Referring  to  Kinley's  estimate  that  check  transactions 
are  at  least  three  times  money  transactions,  he  takes  one 
third  of  143  billions,  or  47.7  billions,  as  the  amount  of  money 
transactions.  Estimating  the  amount  of  money  in  circula- 
tion at  1.025  billions  for  1896,  he  divides  47.7  by  1.025 
and  obtains  (p.  114)  47  times  a  year  as  the  velocity  of  circu- 
lation of  money.  This  figure,  as  we  shall  see,  is  probably 
nearly  three  times  too  large,  the  error  arising  from  the  fact  that 
Professor  Kemmerer  does  not  accept  the  opinion  expressed 
by  Professor  Kinley  that  his  (Kinley's)  estimate  for  the  per- 
centage of  check  circulation  in  1896  was  a  "safe  minimum," 
but  expressed  the  contrary  opinion  that  it  was  rather  a  safe 
maximum.  We  shall  give  reasons  for  believing  that  Kinley 
was  quite  right  in  concluding  that  the  estimate  of  check  trans- 
actions at  three  fourths  of  total  transactions  was  a  "safe 
minimum."  The  calculations  which  we  shall  presently  offer 
prove  nine  tenths  rather  than  three  fourths  to  be  the  probable 
figure. 

Professor  Kemmerer,  as  already  indicated,  estimates  check 

430 


Sec.  1]  APPENDIX   TO    CHAPTER   XII  431 

transactions  (what  we  have  called  M'V)  at  143  billions  in 
1896.  For  other  years  than  1896,  there  being  no  corre- 
sponding data,  he  estimates  check  transactions  by  assuming 
that  bank  clearings  are  always  35  per  cent  thereof  (p.  118). 
He  makes  no  attempt  to  estimate  M'  (bank  deposits)  and  F' 
(their  velocity)  separately.  The  volmne  of  trade  (T)  Pro- 
fessor Kemmerer  estimates  relatively  (i.e.  he  estimates  what 
we  have  called  Q  in  the  Appendix  to  Chapter  X).  This  is 
confessedly  one  of  the  roughest  parts  of  all  his  estimates. 
He  seeks  to  get  as  many  indicators  as  possible  of  the  growth 
of  trade  (p.  130),  without  much  regard  to  their  suitability. 
His  indicators  are  fifteen  in  number,  viz.  population,  foreign 
tonnage  entered  and  cleared,  exports  and  imports  of  mer- 
chandise (values),  revenues  of  Post  Office  Department,  gross 
earnings  from  operation  of  railroads  in  the  United  States, 
freight  carried  by  railroads,  receipts  of  Western  Union  Tele- 
graph Company,  consumption  of  pig  iron,  bituminous  coal, 
wheat,  corn,  cotton,  wool,  wines  and  liquors,  and  market 
value  of  reported  sales  on  New  York  Stock  Exchange.  Rep- 
resenting each  of  these  sets  of  figures  by  index  numbers,  he 
takes  their  simple  average  as  the  index  number  of  trade  for 
each  year  in  question. 

Of  course,  as  Professor  Kemmerer  well  realized,  many  of 
these  figures  are  open  to  more  or  less  serious  objections. 
Population  is  a  poor  index  of  trade  when  trade  per  capita  is 
changing.  Values  are  inappropriate  unless  the  prices  are 
supposed  constant,  which  cannot  be  the  case  for  exports  and 
imports,  railroad  earnings,  or  stocks,  and  can  be  only  par- 
tially the  case  for  post  office  revenues  and  telegraph  receipts. 

Having  thus  computed  for  1879-1908  the  various  elements 
theoretically  determining  price  levels  (viz.  MV+M'V  and 
T),  Professor  Kemmerer  uses  these  to  calculate  an  index 
number  of  prices.  The  index  number  thus  calculated  from 
the  other  magnitudes  in  the  equation  of  exchange,  he  calls 
the  "relative  circulation."  He  then  compares  the  figures 
for  relative  circulation  (virtually  from  the  formula  P  = 
(MV  -\-  M'V)  -i-  T)  with  the  actual  statistics  of  price  levels. 


432        THE    PURCHASING   POWER  OF  MONEY     [Append.  XII 


These  directly  calculated  index  numbers  of  prices  he  takes 
as  an  average  of  index  numbers  of  wholesale  prices  (Com- 
mon's figures  and  those  of  the  Bureau  of  Labor,  p.  137), 
wages  (those  of  reports  of  Bureau  of  Labor,  p.  137),  and  of 
the  Industrial  Commission),  and  prices  of  railroad  stocks  (In- 
dustrial Commission  and  Wall  Street  Journal),  weighting 
them  as  follows :  wages,  3  per  cent ;  stocks,  8  per  cent  ; 
wholesale  commodities,  89  per  cent. 

The  two  sets  of  figures  —  "relative  circulation"  and  "gen- 
eral prices"  —  presented  visually  by  curves  (p.  149),  show 
a  general  agreement. 

§  2  (to  Chapter  XII,  §  2) 

Method  of  Calculating  M 

The  estimates  for  M,  or  money  in  circulation  in  the  United 
States,  are  based  on  the  reports  of  Comptroller  of  the  Cur- 
rency.    The  calculations  are  shown  in  the  following  table  :  — 

Money  in  the  United  States,  etc.  (in  Billions  of  Dollars) 


(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

ai 

«il 

CQ 

2! 

2  «  S  z 

•^  [d  K  ^ 

m  2 

o  2  o 
ca  Q  as 

& 

^a 

tJ 

fifi^ScQ 

p3  0 

oS" 

YSAB 

se 

Z  » 

2:  a 

a  -.  a 

t.  a 

2B 

^  a 

^r. 

i»  H 

f-5 

IhS 

o  5ft  >- 

w  a 

>-Za 

u  ^ 

a  K-"? 

»  5 

a  o 

■^  w  °  s 

a    «^^ 

a  ^  2; 

5-  ^ 

§1 

w  2  z  3 

t3WO§ 

hi 

1896  .     . 

1.80 

1.74 

.29 

.53 

8.4% 

.58 

.87 

1897  .     . 

1.91 

1.83 

.27 

.63 

8.4% 

.68 

.88 

1898  .     . 

2.07 

1.94 

.24 

.69 

7.7% 

.74 

.96 

1899  .     . 

2.19 

2.09 

.29 

.72 

6.7% 

.77 

1.03 

1900  .     . 

2.34 

2.25 

.28 

.75 

6.4% 

.80 

1.17 

1901  .     . 

2.48 

2.37 

.31 

.79 

5.4% 

.84 

1.22 

1902  .     . 

2.56 

2.45 

.31 

.84 

5.3% 

.88 

1.26 

1903  .     . 

2.68 

2.59 

.32 

.85 

5.2% 

.89 

1.38 

1904  .     . 

2.80 

2.68 

.28 

.98 

4.5% 

1.03 

1.37 

1905  .     . 

2.88 

2.77 

.29 

.99 

3.9% 

1.03 

1.45 

1906  .     . 

3.07 

2.97 

.33 

1.01 

3.4% 

1.05 

1.59 

1907  .     . 

3.12 

3.12 

.34 

1.11 

4.2% 

1.15 

1.63 

1908  .     . 

3.38 

3.38 

.34 

1.36 

3.8% 

1.41 

1.63 

1909  .     . 

3.41 

3.41 

.30 

1.44 

2.8% 

1.48 

1.63 

Sec.  2]  APPENDIX   TO    CHAPTER   XII  433 

Column  (2)  gives  the  money  in  the  United  States  in  the  middle 
of  each  calendar  year  according  to  the  official  estimates  of  the 
director  of  the  mint.  In  1907  these  official  estimates  were 
corrected  by  subtracting  an  estimated  error  of  $135,000,000 
from  the  gold  believed  to  be  in  the  United  States,  this  cor- 
rection being  made  in  view  of  the  investigations  of  Maurice 
L.  Muhleman.  The  mint  corrections  were  made,  however, 
only  for  the  ends  of  calendar  years. ^  In  order  to  make  the 
corrections  apply  to  the  middle  of  a  given  calendar  year,  the 
corrected  figures  for  gold  in  the  United  States  at  the  begin- 
ning and  end  of  it  were  averaged.  The  average  thus  obtained 
was  assumed  to  be  the  corrected  figure  for  gold  at  the  middle 
of  the  year.  This  corrected  figure  was  then  compared  with  the 
official  figure  for  gold  for  the  middle  of  the  year  and  the  differ- 
ence assumed  to  be  the  correction  for  that  date.  This  correc- 
tion was  then  deducted  from  the  figures  for  money  in  the 
United  States  given  in  column  (2)  above.  We  thus  obtain  the 
figures  in  column  (3).  Mr.  Muhleman  has  made  independent 
corrections  for  the  middles  of  the  years  1896-1900  inclusive. 
These  are  slightly  smaller  than  those  calculated  from  the  mint 
figures  as  given  above,  the  differences  being  in  successive 
years,  .05,  .03,  .00,  .03,  .05.  Columns  (4)  and  (5)  of  our  table 
give  the  money  in  the  federal  treasury  and  the  money  re- 
ported in  banks  as  stated  in  the  annual  reports  of  the  Comp- 
troller of  the  Currency.  Column  (6)  gives  the  estimated  per- 
centage not  reported.  This  estimate  is  found  by  assuming 
that  the  unreported  reserves  bear  the  same  ratio  to  there- 
ported  reserves  as  unreported  deposits  bear  to  reported  de- 
posits, the  latter  ratios  being  calculated  from  the  table  given 
in  the  next  section  (§  3)  of  this  Appendix. 

This  estimated  percentage  being  calculated  and  the  correc- 
tion found  by  it  being  added  to  the  money  in  reporting  banks, 
(column  5),  we  get  the  total  estimated  money  in  banks, 
(column  7).  Column  (8)  is  then  found  by  subtracting  from  the 
corrected  money  in  the  United  States  (as  given  in  column  3), 

'  See  Report  of  the  Director  of  the  Mint,  1907,  p.  87. 
2f 


434       THE   PURCHASING   POWER  OF  MONEY     [Append.  XII 

the  sum  of  the  money  m  treasury  (column  4),  and  estimated 
money  in  banks  (column  7).  These  estimates  of  money  in 
nonreporting  banks  are  of  course  subject  to  some  error;  but 
even  a  50  per  cent  error  in  the  largest  of  them  would  not 
affect  the  last  column  much  more  than  2  per  cent.  A  more 
important  possible  source  of  error  is  in  column  (2),  which  de- 
pends upon  hypothetical  estimates  of  gold  in  the  United 
States.  Mr.  Muhleman  writes  me  that  in  his  opinion  the 
corrections  made  by  the  Mint  Bureau  are  not  adequate. 
The  corrections  as  made  by  that  Bureau  and  here  adopted 
affect  several  of  the  figures  in  column  (8)  by  as  much  as  10 
per  cent.  The  errors  in  these  corrections  would  presumably 
be  much  smaller  than  this.  There  are  few  other  sources  of 
error  and,  taking  all  things  into  account,  it  seems  likely  that 
the  results  are  in  general  trustworthy  —  subject  to  a  prob- 
able error  of  perhaps  2  or  3  per  cent.  This  is  fair  accuracy 
as  ordinary  statistics  go. 

§  3  (to  Chapter  XII,  §  2) 

Method  of  Calculating  M' 

The  calculations  for  obtaining  M',  or  individual  deposits 
subject  to  check,  are  shown  in  the  table  on  page  49. 

The  figures  of  column  (2)  are  those  of  "Individual  Depos- 
its" taken  from  the  annual  reports  of  the  Comptroller  of  the 
Currency  (see  Report  for  1909,  pp.  64-66).  For  the  years 
1896-1899  correction  is  made  for  deposits  of  trust  companies 
and  savings  banks  misclassified  as  individual  deposits.  Prior 
to  1900  many  banks  included  such  deposits  of  bankers  as 
individual  deposits.  They  should  be  deducted  because  such 
deposits  in  one  bank  by  other  banks  are  not  generally  used 
for  commercial  purchases,  but  for  banking  operations.  These 
deposits,  to  be  deducted  from  column  (2),  are  given  in  col- 
umn (3). 

The  figures  in  cloumn  (3)  are  estimates  baaed  on  the  fact 
that  the  deposits  of  savings  banks  and  trust  companies  in 
national  banks  are  (whenever  comparison  is  possible,  viz. 


Sec.  3] 


APPENDIX   TO    CHAPTER   XII 


435 


1900-1908)  found  to  be  approximately  equal  to  the  deposits 
of  state  banks  in  national  banks.  As  the  state  bank  figures 
are  available  for  1896-1899,  they  are  taken  in  Ueu  of  the 
missing  trust  and  savings  figures.  Since  the  original  edition 
of  this  book  was  printed,  consultation  with  the  Comptroller 
has  convinced  the  writer  that  these  corrections  are  too  large 
and  that  it  would  have  been  better  to  have  omitted  them 
altogether.  They  are  retained,  however,  in  order  not  to 
necessitate  numerous  changes  in  the  plates.  Fortunately, 
as  will  be  seen  on  page  492,  the  net  error  thus  retained  is 
very  small. 

iNDivmuAL  Deposits,  Subject  to  Check  (in  Billions  of  Dollars) 


(1) 

(2)J 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

H 

o 

»       OQ  re 
Q  tH  O  M 

«5 

00 

o 

> 

iO  '-' 

KM 

00 

KM 

Q 

B  BS  >■  l) 

2;  S 
t>  9 

< 

OS 
Ui  o 

n  M 

g^5 

Yeab 

< 
g 
> 

a!  o  S 
-<  "  Z  z 
J  m  •<  S 
O  E-     .    . 

'^  a. 

bQ 

<  a 

g 

00 
00   00 

ooW 

li 

n  •< 

2q  00 

Y«  o 

.-,0  w 

X  jO 

a 
2; 

00  5!  (B  a! 

SSopa 

CO   o 

w2 

o  a 
X  J 
WO 

1  «  J 
S5S 

0  s) 

1896     .     .     . 

4.95 

.16 

.40 

1.91 

.11 

3.17 

85 

2.68 

1897     . 

5.10 

.21 

.41 

1.94 

.11 

3.25 

86 

2.80 

1898    . 

5.69 

.25 

.42 

2.07 

.16 

3.63 

88 

3.19 

1899    . 

6.77 

.33 

.44 

2.23 

.27 

4.38 

89 

3.90 

1900    . 

7.24 

.45 

2.45 

.18 

5.06 

87 

4.40 

1901     . 

8.46 

.46 

2.60 

.36 

5.96 

86 

5.13 

1902    . 

9.10 

.48 

2.75 

.36 

6.47 

84 

5.43 

1903     . 

9.55 

.50 

2.93 

.25 

6.87 

83 

5.70 

1904    . 

10.00 

.45 

3.06 

.23 

7.16 

81 

5.80 

1905    . 

11.35 

.44 

3.26 

.36 

8.17 

80 

6.54 

1906    . 

12.22 

.41 

3.48 

.40 

8.75 

78 

6.84 

1907    . 

13.10 

.55 

3.69 

.33 

9.63 

74 

7.13 

1908    . 

12.78 

.49 

3.66 

.29 

9.30 

71 

6.60 

1909    . 

14.01 

.39 

3.91 

.38 

10.11 

67 

6.75 

After  deducting  the  correction  of  colunm  (3),  our  next 
step  is  to  add  the  correction  of  column  (4),  the  estimated 
deposits  unreported. 

The  figures  for  nonreporting  banks  for  1900  and  1902-1909 


436       THE    PURCHASING    POWER   OF  MONEY     [Append.  XII 

are  the  official  estimates  of  the  Comptroller  of  the  Currency. 
(Those  for  1900  and  1902  are  entered  in  the  Comptroller's 
tables  under  the  rubric  "reporting  capital  only"  instead  of 
"nonreporting,"  but  I  am  assured  by  the  Comptroller's 
office  that  this  is  a  distinction  without  a  difference.)  The 
figure  for  1901  is  interpolated  between  those  of  1900  and  1902. 
The  figure  for  1896  is  estimated  by  the  aid  of  two  assumptions. 
The  first  assumption  is  that  the  unreported  deposits  in  that 
year  should  be  larger  relatively  to  all  deposits  than  was  the 
case  in  1903,  as  the  table  shows  that  the  farther  back  we  go 
the  larger  is  the  percentage  of  missing  deposits.  This  con- 
sideration indicates  that  the  correction  exceeds  .28.  The 
second  assumption  is  that  the  correction  should  be  less 
absolutely  than  in  later  years ;  because  the  total  deposits  were 
then  much  less  than  later;  and  because  the  official  figures 
in  column  (4),  viz.  those  for  1900  and  1902-1909  show,  as  we 
proceed  backward  in  time,  that  there  is  a  shght  tendency  for 
them  to  grow  less  in  absolute  amount.  (The  chief  exception 
is  for  1909,  when  the  special  investigation  of  April  28  reached 
an  unusual  degree  of  accuracy.)  This  consideration  would 
make  the  correction  less  than  .50.  Therefore,  between  .28 
and  .50  we  select  .40  as  a  rough  mean.  The  error  involved  is 
not  likely  to  affect  the  final  column  more  than  3  or  4  per 
cent.     The  corrections  for  1897-1899  are  interpolated. 

Column  (5)  gives  a  correction  to  be  subtracted,  viz.  the 
deposits  in  savings  banks.  These  deposits,  by  the  nature 
of  the  case,  are  not  used  as  a  circulating  medium,  but  are 
nevertheless  included  in  the  official  "individual  deposits" 
of  column  (2).  The  item  for  1909  as  here  given  includes, 
besides  the  reported  figures,  an  additional  item  of  .20  (i.e. 
$200,000,000),  being  the  savings  accounts  of  the  state 
banks  of  Illinois.  The  inclusion  of  this  Illinois  item  is 
simply  in  order  to  make  the  figures  for  1909  comparable 
with  those  of  the  preceding  years  in  which  the  same  item 
had  always  been  included  (see  Comptroller's  Report,  1909, 
pp.  43-44). 

Column  (6)  contains  another,  though  small,  subtractive 


Sec.  3]  APPENDIX  TO   CHAPTER   XII  437 

correction,  viz.  the  "exchanges  for  clearing  house."  In 
general,  these  exchanges  represent  checks  which  have  been 
deposited  by  the  persons  receiving  them  but  which  have  not 
yet  reached  the  home  bank  and  been  charged  against  the  per- 
sons who  drew  them.  Any  one  (except  a  sharper  or  a 
blunderer)  will,  as  soon  as  he  has  drawn  a  check,  deduct  the 
amount  of  it  (say  $100)  from  his  deposit  balance  and  refrain 
from  drawing  against  it  again.     Such  a  person  —  say  Smith 

—  regards  the  $100  as  transferred  to  his  drawee  —  say  Jones 

—  and  no  more  Smith's  than  money  would  be  which  he  had 
paid  out.  But  it  takes  time  before  the  bank  on  which  Smith 
draws  knows  of  this  transfer  of  Smith's  deposits  to  Jones. 
In  the  meantime  the  bank  books  still  include  this  $100  among 
Smith's  deposits.  The  total  figure  for  deposits  is  not  dis- 
turbed by  the  inclusion  of  the  $100  in  Smith's  account  pro- 
vided it  is  not  included  in  Jones's  account  also.  But  when 
Jones  deposits  the  check  in  his  bank,  this  (Jones's)  bank  adds 
$100  to  Jones's  account  before  Smith's  bank  can  deduct  it  from 
Smith's  account.  That  is,  the  $100  is  temporarily  counted  as 
both  Smith's  and  Jones's.  If  both  sides  of  this  transfer  were 
recorded  at  the  same  time,  there  would  be  no  double  counting. 
But  until  the  check  reaches  Smith's  bank  the  only  record  of 
the  deduction  which  should  be  made  from  Smith's  account  is 
in  the  ''exchanges  for  clearing  house"  which,  accordingly,  we 
must  deduct  in  our  statistics. 

These  figures,  however,  have  to  be  estimated.  Only  for 
April  28,  1909,  are  they  given  for  all  banks,  the  figures  being 
those  of  the  special  Report  of  the  Monetary  Commission  al- 
ready referred  to.  Of  this  amount,  four  fifths  are  of  national 
banks ;  and  as  national  banks  report  annually  their  exchanges 
against  clearing  houses,  we  assume  that  the  total  each  year 
is  five  fourths  of  that  reported  by  the  national  banks  (see 
Comptroller's  Report,  1908,  pp.  514-522).  The  whole  correc- 
tion is  so  small  that  any  error  in  this  assumed  ratio  is  quite 
negligible  in  the  final  result. 

Column  (7)  is  derived  by  applying  to  column  (2)  the  above 
mentioned  corrections,  —  deduction  of  items  in  column  (3), 


438       THE    PURCHASING   POWER  OF  MONEY     [Append.  XII 

addition  of  those  of  column  (4),  deduction  of  column  (5),  and 
deduction  of  column  (6). 

But  even  yet  we  have  not  reached  the  desired  item, — deposit 
currency,  or  deposits  subject  to  check.  The  net  individual 
deposits  which  we  have  estimated  include,  not  only  current 
accounts,  but  deposits  on  certificate  and  other  deposits  which 
are  considered  investments  rather  than  media  of  exchange. 
The  first  published  attempt  to  give  the  true  deposits  subject  to 
check  is  that  of  the  National  Monetary  Commission.  In  their 
valuable  special  Report  as  of  April  28, 1 909,  constructed  through 
the  Comptroller  of  the  Currency,  the  checkable  deposits  are 
given  as  6.94  billions.^  This  6.94  is  subject  to  an  addition 
for  " nonreporting  banks"  and  a  deduction  for  "exchange 
against  clearing  house."  The  unreported  deposits  of  all 
kinds  are  estimated  for  1909  in  the  table  at  .39,  of  which,  by 

proportion,  only  — —  of  .39  or  .19,  is  probably  checkable. 

The  .38  exchanges  against  clearing  houses  must  be  assumed  to 
be  almost  wholly  against  deposits  subject  to  check.  The  net 
corrected  figure  is  therefore  6.94  +  .19  —  .38  or  6.75  billions 
as  the  checkable  deposits  in  1909.  These  constitute  about 
67  per  cent  of  the  "net  individual  deposits  "  of  column  (7). 

This  figure  for  checkable  deposits  in  1909  is  found  at  the 
bottom  of  column  (9)  in  the  table.  As  it  is  only  67  per  cent 
of  the  net  individual  deposits,  and  as  it  could  not  be  assumed 
that  the  same  ratio  obtained  for  other  years,  I  was  unwilling 
to  guess  at  the  deposits  subject  to  check  for  these  other  years 
without  further  light.  Accordingly  I  wrote  to  Mr.  A.  Piatt 
Andrew,  then  Director  of  the  Mint,  and  asked  him  whether, 
in  his  capacity  as  advisor  to  the  Monetary  Commission,  he 
could  not  have  a  search  made  among  the  Comptroller's  rec- 
ords for  1896  and  a  few  other  years  in  order  to  obtain  the 

>  See  Senate  Document,  225,  61st  Congress,  2d  Session,  Special 
Report  from  Banks  of  the  United  States,  April  28,  1909,  p.  261  ;  also 
Report  of  Comptroller  of  the  Currency,  1909,  p.  835.  The  figures  are 
exclusive  of  Hawaii,  Porto  Rico,  and  the  Philippines,  although  the 
8tun  thus  excluded  is  scarcely  appreciable. 


Sec.  3]  APPENDIX  TO   CHAPTER   XII  439 

corresponding  ratio  for  such  years.  Through  his  kindness 
and  that  of  the  Commission  and  Comptroller,  in  acceding  to 
my  request,  it  has  been  made  possible  to  work  out  the  corre- 
sponding ratio  for  1896  as  85  per  cent;  for  1899  as  89  per  cent; 
and  for  1906  as  78  per  cent. 

Mr.  Andrew  gives  4.97  billions  as  the  total  (uncorrected) 
deposits  of  all  banks  as  of  July  14,  1896.  This  figure  is 
slightly  more  complete  than  what  I  had  already  used  from  the 
Comptroller's  Report  (viz.  4.95),  doubtless  because,  for  this 
particular  inquiry,  a  larger  number  of  banks  were  included 
than  had  originally  been  used  in  the  Comptroller's  tables. 
Mr.  Andrew  gives  the  checkable  deposits  as  2.59  billions. 
This  figure  is  subject  to  two  corrections:  one  to  account  for 
unreporting  banks,  and  one  to  account  for  exchanges  for  clear- 
ing house.  We  have  estimated  the  deposits  of  nonreporting 
banks  at  .40 ;  and,  since  Mr.  Andrew  has  discovered  in  such 
banks  .02  more  total  deposits  (4.97)  than  the  Comptroller 
reported,  we  must  assume  that  there  are  .02  less  unreported 
deposits  in  his  figures  than  in  the  Comptroller's.  This  would 
make  the  estimated  unreported  deposits  for  Andrew's  figures 
.38  instead  of  .40  which  we  assumed  for  the  Comptroller's. 
The  part  of  this  ascribable  to  the  deposits  subject  to  check 

(2.59)  is  ^^  X  .38  or  .20.     This  is  the  first  (and  additive) 
4.97 

correction.     The  second  (and  subtractive)  correction  is  the 

exchanges  for  clearing  house,  viz.  .11.      The  final  corrected 

figure  is  therefore  2.59  +  .20  -  .11  or  2.68.      The  ratio  of 

2  68 
this  to  the  "net  deposits"  is  -^  or  85  per  cent. 

For  1899,  Andrew's  figures  for  total  net  deposits  are  4.38  and 
for  checkable  deposits  4.09.  His  figures  for  total  deposits 
(7.07)  are  .30  completer  than  those  of  the  Comptroller  em- 
ployed in  the  first  column  of  the  above  table,  and  thus  reduce 
the  estimate  for  nonreporting  banks  apphcable  to  Andrew's 

4  OQ  M 

figures  from  .44  to  .14,  of  which  -^  X  .14  or  .08  are  ascnb- 
*  7.07 

able  to  the  deposits  subject  to  check.     The  correction  con- 


440       THE    PURCHASING    POWER   OF   MONEY     [Append.  XII 

sisting  of  exchanges  for  clearing  house  is  .27.  The  figures 
for  checkable  deposits  are  therefore  4.09  +  .08  —  .27  or 
3.90,  which  is  89  per  cent  of  the  "net  deposits"  (4.38). 

For  1906  Andrew's  figures  for  total  net  deposits  are  8.75 
and  for  checkable  deposits,  6.90.  His  figures  for  total 
deposits  (12.37)  are  less  complete  than  those  of  the  Comp- 
troller, thus  increasing  the  estimate  for  unreporting  banks 

apphcable  to  his  figures  from  .41  to  .61,  of  which  X  .61 

or  .34  are  ascribable  to  the  deposits  subject  to  check.  The 
exchanges  for  clearing  house  were  .40.  The  figures  for  check- 
able deposits  are  therefore  6.90  +  .34  —  40  or  6.84,  which  is 
78  per  cent  of  the  "net  deposits"  8.75)  We  thus  have 
figures  for  column  (9)  and  column  (8)  for  the  years  1896, 
1899,  1906,  1909. 

If  now,  for  intervening  years,  we  interpolate  evenly  between 
these  percentage  figures  for  the  years  1896,  1899,  1906,  1909, 
we  shall  have  column  (8)  of  the  preceding  table. 

Column  (9)  may  next  be  formed  for  the  remaining  years 
by  applying  the  percentages  in  column  (8)  to  the  net  indi- 
vidual deposits  in  column  (7) .  Thus  the  table  is  made  com- 
plete. 

The  results  are  of  course  subject  to  a  probable  error  which, 
however,  is  believed  to  be  only  some  2  or  3  per  cent  for 
the  years  1896,  1899,  1906,  1909,  and  perhaps  double  as 
much  for  years  midway  in  the  intervals  between  these  four 
years. 

It  seems  strange,  since  so  much  has  been  said  of  the  relative 
importance  of  check  and  money  circulation,  that  no  attempt 
has  previously  been  made  to  estimate  or  record  the  volume  of 
the  currency  which  circulates  by  check.  This  currency  and 
its  circulation  are  of  many  times  the  statistical  importance  of 
money  and  its  circalation.  Our  wonder  is  the  greater  when 
we  consider  that  "  deposits  subject  to  check"  have  been  regu- 
larly reported  by  individual  banks  to  the  Comptroller  of 
the  Currency.  The  pubUshed  figures  began  in  the  '60's  to 
omit  this  category  and  lump  all  "individual  deposits"  to- 


Sec.  4]  APPENDIX  TO   CHAPTER   XII  441 

gether,  and  subsequent  reports  have  simply  followed  the  prec- 
edent thus  established.  The  present  Comptroller  states  that 
he  intends,  hereafter,  to  separate  the  item  of  deposits  subject 
to  check ;  so  that  we  may  hope  from  now  on  to  have  annual 
returns  of  the  checkable  deposits.  We  shall  then  know  each 
year  the  magnitude  of  that  item  in  our  circulatory  medium 
which,  as  we  shall  see,  does  nine  tenths  of  the  exchange 
work  of  the  coimtry. 

§  4  (to  Chapter  XII,  §  3) 
Method  of  Calculating  M'V  for  1896  and  1909 

According  to  the  Comptroller's  Report  for  1896,  the  total 
sum  (money  and  checks)  deposited  in  all  reporting  banks  on 
the  settling  day  nearest  July  1,  1896,  was  303  millions.  Pro- 
fessor Kemmerer's  allowance  for  nonreporting  banks  (op.  cit., 
pp.  110-111)  brings  the  figures  up  to  506  milhons.  The  pro- 
portion of  checks  found  in  all  deposits  reported  Avas  92.5  per 
cent,  which,  if  appUed  to  the  estimated  506  millions  of  total 
deposits,  will  give  468  millions  as  the  total  checks  deposited 
in  one  day.  But  July  1,  being  a  first  day  of  the  month, 
would  show  exceptionally  large  deposits.  In  order  to  de- 
termine how  much  allowance  to  make  for  this  fact,  I  have 
obtained,  through  the  kindness  of  Mr.  Gilpin  of  the  New 
York  clearing  house,  the  figures  for  the  New  York  clearings  of 
July  2,  1896.  July  2  was  selected  because  the  checks  depos- 
ited in  New  York  July  1  would  appear  in  the  clearing  house 
statistics  of  July  2.  The  clearings  for  July  2  amounted  to 
157  millions,  while  the  daily  average  for  1896  was  only  95 
millions  or  60  per  cent  as  much.  Thus,  the  excessive  clear- 
ings of  July  2  have  to  be  corrected  by  multiplying  by  .60  in 
order  to  reach  a  true  average  for  the  year.  It  is  perhaps  fair 
to  assume  that  the  deposits  made  on  July  1  in  New  York 
require  substantially  the  same  correction.  If  we  could  as- 
sume that  the  abnormality  of  the  day's  deposits  in  the  rest 
of  the  country  were  exactly  like  that  of  New  York,  requiring 
the  same  correction  factor  (.60),  then  this  correction  factoi 


442       THE    PURCHASING    POWER   OP  MONEY     [Append.  XII 

would  apply  to  the  whole  country.  But  this  assumption  we 
cannot  make.  Doubtless  .60  is  too  small  an  estimate  of  the 
true  multiplier  for  the  whole  country  outside  of  New  York. 
The  departure  from  the  average  was  probably  somewhat  less 
than  in  New  York  City. 

That  this  is  the  case  appears  likely  for  various  reasons. 
In  the  first  place  New  York  is  more  sensitive  to  the  varia- 
tions in  business  activity  than  the  country  generally.  Con- 
sistently with  this  view,  we  find  that  the  percentage  fluctua- 
tion in  clearings  from  year  to  year  is  much  greater  in  New 
York  than  in  the  rest  of  the  country.  By  comparing  each 
year  with  the  next,  we  find  this  to  be  true  of  all  except  five  of 
the  twenty-seven  years  from  1883  to  1909  ^  inclusive. 

Again,  the  quarterly  and  semiannual  dividends  would  cut  a 
larger  figure  in  a  financial  center  like  New  York  than  in  other 
places,  in  many  of  which  few  or  no  dividends  are  received. 

Finally,  in  large  cities  like  New  York,  checks  are  deposited 
more  systematically  and  promptly,  so  that  a  fuller  proportion 
of  the  first-of-the-month  checks  received  on  July  1  would  be 
deposited  on  that  day  than  in  a  smaller  community.  In  the 
smaller  community  these  checks  straggle  along  to  banks 
through  several  days  after  being  received,  thus  tending  to 
even  up  the  daily  flow  and  in  particular  to  diminish  the  excess 
on  and  about  July  1.  We  conclude  that  .60  is  a  minimum 
estimate  for  our  multipHer  for  1896. 

Having  obtained  .60  as  a  minimum  estimate,  we  next 
proceed  to  ascertain  a  maximum  estimate.  We  may  be 
reasonably  sure  that  deposits  outside  of  New  York  are  so  far 
subject  to  the  influence  of  quarterly  dividends,  first-of-the- 
month  payments,  etc.,  that  the  volume  of  checks  deposited 
outside  of  New  York  must  to  some  extent  exceed  the  average 
in  1896.  We  need  to  know  to  what  extent  we  are  safe  in 
assuming  that  this  outside  volume  of  checks  deposited  on  the 
day  chosen  exceeded  the  average.     We  can  best  reach  such  a 

'  See  Financial  Review  (the  Annual  of  the  Commercial  and 
Financial  Chronicle),  1906,  p.  26  and  1910,  p.  33. 


Sec.  4]  APPENDIX  TO   CHAPTER   XII  443 

safe  estimate  by  means  of  some  data  on  clearing  houses  in  the 
Finance  Report  for  1896  (p.  493,  Comptroller's  Report). 
It  is  there  shown  that  on  July  1,  or  "the  settling  day  nearest 
July  1,"  66  out  of  the  78  clearing  houses  of  the  country  had 
$228,000,000  of  clearings.  We  are  safe  in  assuming  that  the 
country's  total  clearings  on  that  day  were  larger  than  this,  be- 
cause the  returns  as  given  include  only  66  out  of  the  78  clear- 
ing houses  of  the  country ;  and  that  on  the  following  day  they 
were  larger  still,  ^  because  it  was  then  that  occurred  the  bulk  of 
the  heavy  July  1  deposits  of  checks.  If  the  $228,000,000  clear- 
ings on  July  1,  1896,  were  representative  for  each  day  of 
1896,  we  could,  simply  by  multipl3dng  by  the  number  of 
setthng  days  of  1896,  305  days,  find  the  total  clearings  of  the 
country.  But  the  result  of  this  multipUcation  is  67.1  bil- 
lions, whereas  the  actual  clearings  of  the  country  for  1896 
were  only  51.2  billions.  This  is  conclusive  evidence  that  the 
clearings  on  July  1,  and  presumably  still  more  those  of  July  2, 
exceeded  the  daily  average  and  need  to  be  reduced  at  least  in 

the  ratio  — —  or  .76. 
67.1 

Hence  the  true  correction  factor  must  he  between  .60  and 
.76.  Sphtting  the  difference  we  have  .68  as  an  estimate  which 
cannot  be  far  from  the  correct  figures  on  either  side ;  espe- 
cially as  .60  and  .76  are  so  very  safe  or  extreme  limits.  Fig- 
ures very  near  either  of  them  are  improbable.  The  'probable 
error  is  simply  set  at  5  or  6  per  cent. 

We  turn  now  to  similar  calculations  for  1909.  At  my 
request  Professor  Weston  of  the  University  of  Illinois, 
through  the  kindness  of  Professor  Kinley,  has  used  sub- 
stantially the  same  method  for  estimating  the  check  circula- 

1  Convincing  proof  that  the  clearings  on  July  2  exceeded  those 
on  July  1  is  afforded  by  the  fact  that  whereas  the  New  York  state 
clearings  for  July  1, 1896,  were  $140,000,000,  as  given  in  the  Comp- 
troller's Report  for  1896  (p.  494),  the  New  York  City  clearings 
alone  on  July  2  were  $157,000,000. 

For  New  York  City  the  clearings,  as  Mr.  Gilpin  of  the  New  York 
clearing  house  has  informed  me,  were  far  larger  on  July  2,  1896, 
than  on  July  1,  the  two  figures  being  157  and  138  millions  respectively. 


444        THE    PURCHASING    POWER  OF  MONEY     [Append.  XII 

tion  of  1909  based  on  Kinley's  investigation  '  of  that  year  for 
March  16.  Professor  Weston  estimates  the  total  check  de- 
posits of  March  16,  1909,  at  1.02  billions.  This  is  below  the 
daily  average.  A  proof  of  this  is  found  in  the  clearings  of  the 
New  York  clearing  house  on  March  17,  which  reflect  the  de- 
posits made  in  New  York  banks  on  the  previous  day;  these 
were  268  millions,  which  was  not  representative  of  the  year, 
as  the  average  daily  clearings  were  much  greater,  being  342 
millions,  or  28  per  cent  greater  than  those  of  March  17. 
1.28  is  therefore  the  correction  multiplier  we  would  apply  if 
we  could  trust  New  York  clearings  to  be  a  faithful  barometer 
for  the  whole  country.  But  since,  as  we  have  seen,  New 
York  is  especially  sensitive  to  speculative  and  other  varia- 
tions in  banking  operations,  and  as  a  part  is  usually  more 
variable  than  the  whole,  it  is  reasonable  to  assume  that  the 
abnormality  we  find  in  New  York  of  the  deposits  on  March 
16  exaggerates  the  abnormality  of  that  day  for  the  country 
at  large,  and  tiiat  the  correction  multiplier  should  be  less 
than  1.28.  In  order  to  set  a  safe  lower  limit,  we  may  see 
what  figure  would  result  from  the  extreme  assimaption  that 
outside  of  New  York  the  day's  deposits  on  March  16,  1909, 
were  exactly  the  same  as  the  daily  average  for  the  year. 
We  can  make  a  fairly  good  estimate  of  the  resulting  correc- 
tion factor  from  the  table  on  page  59. 

This  table  is  constructed  from  data  taken  from  Kinley's 
report  to  the  Monetary  Commission  on  Credit  Instruments 
(pp.  182,  186)  together  with  the  estimated  corrections  for  the 
whole  country's  check  deposits  made  by  Professor  Weston. 

The  figure  for  deposits  in  New  York  City  is  given  for  March 
16,  1909.  Deducting  these  figures  from  those  estimated  by 
Weston  for  the  entire  country,  we  have  the  deposits  (786) 
outside  New  York.  But  the  daily  average  in  New  York  has 
been  shown  to  be  probably  28  per  cent  higher,  or  306.  These 
figures,  added  to  those  for  deposits  outside  New  York  (786), 

^  Kinley,  The  Use  of  Credit  Instruments  in  Payments  in  the  United 
Slates,  National  Monetary  Commission,  61st  Congress,  2d  Session, 
Doc.  No.  399,  1910. 


Sec.  4] 


APPENDIX   TO    CHAPTER   XII 


445 


give  the  daily  average  for  the  entire  country,  on  the  assump- 
tion that  only  New  York  City  was  abnormal  on  the  day  se- 
lected. The  result  (1092),  compared  with  the  actual  deposits 
on  the  day  selected  (1025),  shows  the  correction  factor  on  the 
assumption  that  only  New  York  was  abnormal.  This  factor 
is  1.07.  This  furnishes  a  lower  limit  for  the  correction  factor 
we  are  seeking. 

Checks  Deposited  (in  Millions) 


(1) 


March  16,  1909 

Daily  average  if  New  York  were  alone 
abnormal 

Ratio  average  to  actual  = =  1.07 

1025 


(2) 


New  York 
City 


239 
306 


(3) 

Outside 

New  York 

City 


786 
786 


(4) 

Total 
U.S. 


1025 
1092 


Splitting  the  difference  between  our  extreme  Hmits,  1.07 
and  1.28,  we  get,  as  our  estimate  of  the  correction  factors, 
1.17  in  1909  as  compared  with  .68  for  1896.  The  range  of 
possible  error  on  either  side  is  about  10  for  1909  and  8  for 
1896.  As  the  limits  are  all  very  extreme,  the  probable  error 
must  be  much  less  —  perhaps  half  as  much.  We  may  judge 
that  the  correction  factors,  .68  and  1.17,  are  probably  correct 
within  5  or  6  per  cent. 

We  conclude,  then,  that  the  468  millions  estimated  as  the 
actual  check  deposits  made  on  July  1,  1896,  must  be  multi- 
plied by  .68  in  order  to  obtain  the  estimated  average  daily 
deposits  in  1896.  The  result  is  318  millions ;  which,  multi- 
plied by  the  305  (setthng  days),  gives  97.0  billions  as  our  esti- 
mate for  the  check  transactions  in  the  United  States  for  the 
year  1896. 

Likewise,  multiplying  the  estimated  volume  of  actual 
check  transactions  in  the  United  States  on  March  16,  1909 
(viz.  1025  millions) ,  by  the  correction  factor,  1.17,  we  obtain 


446       THE   PURCHASING   POWER  OF  MONEY     [Append.  XII 

1.20  billions  as  the  estimated  daily  average  check  deposits 
and  transactions.  Multiplying  this  by  303  (the  number  of 
clearing  days  of  the  New  York  clearing  house  and  presumably 
the  average  number  of  banking  days  in  the  country),  we 
obtain  364  billions  as  our  estimate  of  the  check  transactions 
in  the  United  States  in  1909. 

§  5  (to  Chapter  XII,  §  3) 
Method  of  Calculating  M'V  for  1897-1908 

Although  New  York  clearings  constitute  two  thirds  of  all 
clearings  for  the  country,  it  cannot  be  imagined  that  the 
check  transactions  in  and  about  New  York  form  two  thirds 
of  the  check  transactions  of  the  United  States.  We  have 
already  seen  that  the  reported  check  deposits  in  New  York 
on  March  16,  1909,  amounted  to  239  millions.  This  figure, 
being  for  New  York,  is  probably  nearly  complete  and  indi- 
cates, as  we  have  seen,  an  estimated  average  for  the  daily 
deposits  in  New  York  City  in  1909  of  306  millions.  This 
gives  306  X  303  or  93  bilhons  for  New  York  City,  for  the 
entire  year.  Our  estimate  for  the  entire  country  was  364 
billions,  leaving  271  billions  outside  of  New  York  City.  Let 
us  compare  these  estimated  figures  for  checks  deposited  with 
the  figures  for  clearings.  The  New  York  clearings  in  1909 
amounted  to  104  billions  and  those  outside  New  York,  to 
62  billions. 

The  New  York  clearings  (104)  thus  exceed  the  New  York 
check  deposits  (93),  probably  because  the  clearings  on  ac- 
count of  outside  banks  include  clearings  representing  bank- 
ing transactions  as  distinguished  from  commercial  trans- 
actions,  since  New  York  City  is  the   chief  central  reserve 

93 

city.     The  New  York  City  deposits  were   thus  only  — — ■ 

or  about  90  per  cent  of  the  New  York  clearings.     Outside  of 

New  York,  on  the  other  hand,  the  deposits  far  exceeded  the 

271 
clearings,  being  in  the  ratio  — -  or  4.4.    These  ratios  between 


Sec.  5]  APPENDIX  TO    CHAPTER   XII  447 

check  transactions  and  clearings,  viz,  .90  for  New  York  and 
4.4  for  "outside,"  would  indicate  that  the  pubhshed  figures 
for  clearings  should  be  weighted  in  the  ratio  of  4.4  to  .9  or 
about  5  to  1.  That  is,  on  the  basis  of  1909  figures,  five  times 
the  outside  clearings  plus  once  the  New  York  clearings  should 
be  a  good  barometer  of  check  transactions. 

Of  1896,  unfortunately,  we  lack  the  figures  for  New  York 
City  deposits.  We  have,  however,  figures  for  the  deposits 
in  New  York  state  in  both  1896  and  ,1909 ;  and  a  study  of 
these  figures  indicates  that  the  ratio  of  weighting  for  1896 
should  be  something  over  3  to  1.  Not  to  put  too  fine  a  point 
upon  it,  we  shall  use  the  weighting  5  to  1  for  all  the  years. 
The  difference  in  the  results  between  this  system  of  5  to  1  and 
a  system  of  3  to  1,  or  any  intermediate  system,  will  be  small, 
but  5  to  1  is  chosen  because  (1)  the  data  for  1896  on  which  the 
number  3  is  based  are  less  certain  than  those  for  1909,  and 
(2)  the  New  York  clearings  are  not  as  good  a  representative 
of  New  York  deposits  as  the  outside  clearings  are  of  outside 
deposits ;  the  New  York  clearings  being  somewhat  vitiated  by 
an  element  extraneous  to  New  York  and  especially  by  the 
banking  transactions  connected  with  adjustments  of  bank 
reserves.  We  prefer,  therefore,  to  give  as  much  weight  as 
possible  to  the  "outside"  clearings. 

Having  obtained  our  "barometer"  of  check  transactions, 
viz.  New  York  clearings  plus  five  times  outside  clearings,  we 
merely  need  to  multiply  this  by  the  proper  ratio  in  order  to 
obtain  the  check  transactions  themselves.  Absolute  knowl- 
edge of  this  ratio  of  check  transactions  to  the  barometer 
exists  only  for  1896  and  1909,  in  which  years  we  know 
the  check  transactions  as  well  as  the  barometer.  These  ra- 
tios are  .69  and  .88.  But  we  cannot  err  greatly  in  assuming 
that  the  intermediate  years  have  intermediate  ratios,  varying 
regularly  each  year.     The  result  is  the  following  table :  — 


448       THE    PURCHASING   POWER   OF  MONEY     [Append.  XH 
Clearings  as  Barometer  of  Check  Transactions 


(1) 

(2) 

(3) 

(4) 

(5) 

(6)  M'V 

(7)V' 

Year 

New  York 
Clearings 

Outside 

Clearings 

Barometer 
(2)-f-5X(3) 

Ratio  op 
Check 
Trans- 
action TO 
Barometer 

Check 
Trans- 
actions 
(4)  X  (5) 

Velocity 
op  Circd. 

OP  De- 
posits (V) 

(6)  -r-  M' 

1896  . 

28.9 

22.4 

140.9 

.69 

97 

36.2 

1897  . 

33.4 

23.8 

152.4 

.70 

106 

37.9 

1898  . 

42.0 

26.9 

176.5 

.72 

127 

39.8 

1899  . 

60.8 

33.3 

227.3 

.73 

166 

42.6 

1900  . 

52.6 

33.4 

219.6 

.75 

165 

37.5 

1901  . 

79.4 

39.0 

274.4 

.76 

208 

40.6 

1902  . 

76.3 

41.7 

284.8 

.78 

222 

40.9 

1903  . 

66.0 

43.2 

282.0 

.79 

223 

39.1 

1904  . 

68.6 

43.9 

288.1 

.81 

233 

40.2 

1905  . 

93.8 

50.0 

343.8 

.82 

282 

43.1 

1906  . 

104.7 

55.2 

380.7 

.84 

320 

46.8 

1907  . 

87.2 

57.8 

376.2 

.85 

320 

44.9 

1908  . 

79.3 

53.1 

344.8 

.87 

300 

45.5 

1909  . 

103.6 

62.0 

413.6 

.88 

364 

53.9 

As  already  indicated,  only  the  first  and  last  figures  in  column 
(5)  are  independently  calculated,  the  rest  being  interpolated. 
The  other  figures  in  the  table  explain  themselves.  The  last 
column  gives  the  very  important  magnitude  which  we  have 
called  the  velocity  of  circulation  of  bank  deposits  subject  to 
check,  or  the  "  activity  "  of  checkable  accounts.  The  probable 
errors  of  the  last  column  are  believed  to  range  between  about 
5  and  10  per  cent. 

§  6  (to  Chapter  XII,  §  4) 

General  Practical  Formula  for  Calculating  V 
I.    An  Approximate  Formula 

For  the  purpose  of  tracing  the  circulation  of  money,  and 
measuring  it  by  bank  records,  we  may  classify  the  persons 
who  use  money  in  purchase  of  goods  into  three  groups :  — 

1.  Commercial  depositors,  i.e.  all  engaged  in  business  — 
firms,  companies,  and  others  —  who  have  bank  deposits 
mainly  or  wholly  apart  from  personal  accounts. 

2.  All  other  depositors,  chiefly  private  persons. 


Sec.  6]  APPENDIX  TO   CHAPTER   XII  449 

3.  All  who,  like  most  wage  earners,  are  not  depositors  at  all. 

These  three  classes  we  shall  distinguish  as  "Commercial 
depositors,"  "Other  depositors,"  and  " Nondepositors," 
or  C,  0,  and  N.  The  money  in  the  possession  of  "Commer- 
cial depositors"  we  shall  call  "till  money,"  and  the  rest 
"pocket  money." 

The  three  groups  necessarily  include  all  in  the  community 
who  circulate  money.  By  circulating  money  is  meant  ex- 
pending it  in  exchange,  not  for  some  other  circulating  medium, 
as  checks,  but  for  goods. 

The  nature  of  these  three  groups  of  people  must  now  occupy 
our  attention.  In  countries  advanced  in  the  art  of  banking, 
"Commercial  depositors"  include  practically  all  business 
establishments,  and  little  else;  "Other  depositors"  include 
most  persons  in  the  professional  and  salaried  classes  and  pro- 
prietors, and  little  else;  while  the  class  of  " Nondepositors " 
is  almost  coterminous  with  wage  earners. 

It  is  true  that  these  characterizations  of  the  three  classes 
are  not  quite  complete.  "Commercial  depositors,"  for  in- 
stance, do  not  include  some  small  business  dealers,  like  street 
vendors,  for  these  usually  have  no  bank  accounts.  But  the 
number  of  such  is  comparatively  small  in  comparison  with 
the  number  of  business  men  or  corporations  who  do  have  ac- 
counts, and,  what  is  more  to  the  point,  the  business  they  do  is 
still  smaller.  It  follows  that  the  money  they  handle  is  negli- 
gible. In  the  United  States,  at  least,  excepting  those  rural 
parts  of  the  South  and  a  few  other  places  where  the  money 
expenditures  are  very  small,  the  custom  of  having  bank 
accounts  is  practically  universal  among  business  men,  firms, 
and  corporations. 

To  keep  a  bank  account  is,  in  fact,  a  practical  necessity  of 
business.  Without  such  an  account  a  business  man  practi- 
cally deprives  himself  of  three  of  the  most  essential  aids  in 
modern  business:  the  use  of  circulating  credit;  the  use  of 
remittance  by  mail ;  and  the  use  of  time  credit. 

Unless  a  dealer  is  obliged  to  pay  "spot  cash"  or  prefers 
to  do  so  —  and  such  cases  are  both  few  in  number  and  insignif* 
2g 


450       THE    PURCHASING   POWER  OF  MONEY      [Append.  XII 

icant  in  the  amounts  of  money  involved  —  he  will  almost  in- 
variably find  it  easier  to  make  payment  by  check.  More- 
over, the  very  fact  that  most  other  business  men  use  banking 
facilities  creates  in  his  mind  the  desire  to  have  an  account 
himself,  both  because  he  dislikes  to  appear  "different,"  and 
because,  when  others  pay  him  by  checks,  he  finds  it  necessary 
to  cash  these  checks,  —  a  procedure  which  is  always  more 
trouble  than  to  deposit  them. 

Cash  payments  are  especially  inconvenient  when  business 
is  done  at  a  distance.  Remitting  money  by  post,  express,  or 
personal  delivery  is  troublesome,  risky,  and  expensive  as 
compared  with  posting  a  letter  containing  a  check.  Even 
a  post-office  money  order  is  a  clumsy  and  expensive  substi- 
tute, and  its  use  proclaims  the  user  an  insignificant  financial 
factor. 

Again,  a  business  man  without  a  bank  account  cannot  usu- 
ally obtain  time  credit,  either  from  dealers  or  from  banks. 
In  the  United  States  a  bank  likes  to  lend  only  to  its  own  de- 
positors. A  business  man  who  asks  for  a  bank  loan  usually 
meets  with  the  request  to  open  an  account.  If  he  should  seek 
a  loan  from  another  dealer,  as  for  instance,  his  supply  house, 
the  absence  of  a  bank  account  would  arouse  suspicions  as  to 
his  business  standing,  and  might  lead  to  a  refusal. 

These  facts,  confirmed  by  observation  and  inquiry,  have 
led  to  the  belief  that  practically  all  business  transactions  in 
the  United  States,  certainly  over  99  per  cent  (measured,  not 
by  their  number,  but  by  their  aggregate  size),  make  some  use 
of  bank  accounts.  Even  in  localities  where  there  are  no  banks, 
traders  usually  like  to  have  a  bank  account  in  the  nearest 
town,  in  order  to  facilitate  their  dealings  as  purchasers. 
We  conclude,  therefore,  that  the  category  of  "Commercial 
depositors"  coincides  for  all  practical  purposes  with  the  cate- 
gory of  business  establishments. 

"Other  depositors"  include  most  proprietors,  professional, 
and  salaried  persons.  Almost  no  wage  earners  are  included, 
and  almost  no  business  estabhshments  or  business  men  in  a 
business  capacity.     When  a  single  individual  conducts  a  busi- 


Sec.  6]  APPENDIX  TO   CHAPTER   XII  451 

ness,  he  usually  separates  carefully  his  business  self  from 
his  personal  self.  John  Smith,  the  individual,  and  the  John 
Smith  Shop  are  distinct.  The  pocket  money  of  the  one  and 
the  till  money  of  the  other  are  not  often  confused.  Where 
payments  of  money  are  made  from  one  to  the  other,  the  trans- 
action is  regarded  as  of  the  same  nature  as  the  payments  be- 
tween the  shop  and  any  other  person.  Originally,  and  under 
primitive  conditions,  it  is  of  course  true  that  no  such  distinc- 
tion was  observed,  and  even  to-day  the  differentiation  is 
sometimes  unmarked,  e.g.  in  the  case  of  hucksters,  peddlers, 
fruit-stand  dealers,  and  small  country  shopkeepers.  But, 
as  we  have  seen,  these  persons  are  not  usually  depositors 
anyway.  Moreover,  their  number  is  small;  and  since  by  the 
nature  of  the  case  the  money  they  handle  is  also  small,  their 
classification  is,  for  practical  purposes,  a  matter  of  indifference. 
It  is  true  that  occasional  cases  exist  of  ordinary  business  men 
who  have  the  exclusive  ownership  of  a  business  and  do  not 
take  care  to  separate  clearly  their  business  and  their  personal 
accounts.  Yet  we  may,  in  such  cases,  perform  the  separation 
in  thought.  When  such  a  person  withdraws  money  from  his 
till  and  puts  it  in  his  pocket,  we  may  say  his  business  self  has 
paid  his  personal  self  some  dividends  of  the  business.  Like- 
wise, his  checks  drawn  are  usually  distinguishable  as  between 
his  business  or  his  personal  expenses,  even  though  he  him- 
self fails  to  keep  two  separate  bank  accounts.  But  such  cases 
are  rare  and  unimportant,  because  modern  business  of  size  is 
usually  conducted  by  partnerships  and  corporations,  where  a 
strict  separation  of  accounts  is  necessary  to  safeguard  con- 
flicting interests. 

So  much  for  the  line  of  demarcation  between  "Other  de- 
positors" and  "Commercial  depositors."  As  to  the  hne 
separating  "Other  depositors"  and  "Nondepositors,"  it 
should  be  observed  that,  although  "Other  depositors"  in- 
clude most  proprietors  and  professional  and  salaried  persons, 
yet  some  proprietors  and  professional  men,  especially  in  rural 
communities,  and  some  salaried  persons,  chiefly  small  clerks, 
are  "Nondepositors." 


452       THE   PURCHASING   POWER   OF   MO?>rEY     [Append.  XII 

Finally,  "Nondepositors"  consist  chiefly  of  those  who  are 
classed  in  statistics  as  wage  earners.  While  there  are  some 
wage  earners  who  are  depositors,^  they  are  rare;  and  while 
there  are  some  "Nondepositors"  who  are  not  wage  earners, 
especially  (as  just  indicated)  the  agricultural  proprietors 
(farmers)  and  small  clerks,  the  amount  of  money  circulated 
by  them  is  small  in  comparison  with  the  total  circulation. 
While  the  line  separating  wages  and  salaries  is  not  definitely 
marked  in  theory,  it  is  usually  easily  recognized  in  practice. 

Children  under,  say,  twelve  years  need  not  be  included  in 
any  of  the  three  categories,  as  they  are  not  handlers  of  money; 
at  least,  not  to  a  sufficient  degree  to  have  any  appreciable  in- 
fluence on  the  total  circulation. 

We  may  now  picture  concretely  the  main  currents  of  the 
monetary  flow,  including  the  circulation  of  money  in  ex- 
change for  goods.  Figure  18  illustrates  the  three  principal 
types. 

The  corners  of  the  triangle,  C,  0  and  N,  represent  the  three 
groups  of  "Commercial  depositors,"  "Other  depositors," 
and  "Nondepositors,"  and  the  5's  represent  banks.  The 
arrows  represent  the  flow  of  money  from  each  of  these  four 
categories  to  the  others.  Thus  Bo  represents  the  annual  with- 
drawals from  banks  by  "Other  depositors,"  Oc  the  spending 
of  this  withdrawn  money  by  "Other  depositors"  among 
"Commercial  depositors,"  and  C,,  the  return  of  the  money 
from  the  "Commercial  depositiors"  to  the  banks.  This 
circuit  (BoOcCi)  of  three  links  is  very  common,  A  second 
type  of  circuit  is  represented  by  a  chain  of  four  arrows 
(BoOnN.Ch).  It  is  illustrated  by  private  depositors  draw- 
ing money  (Bo),  and  paying  wages  (On)  to  servants  who  in 
turn  spend  the  money  (Nc)  among  tradesmen  who  finally 
deposit  it  (C/,).  A  third  type  of  circuit,  also  fourfold,  is 
represented  by  the  arrows  BcCnNcCh-  It  is  illustrated  by 
commercial  firms  cashing  their  checks  at  banks  (Be)  for  pay 

1  The  term  "depositors,"  as  here  used,  does  not,  of  course,  in- 
clude savings  bank  depositors.  A  savings  bank  is  not  a  true  bank 
of  deposit,  providing  circulating  credit. 


Sec.  6] 


APPENDIX   TO    CHAPTER   XH 


453 


rolls,  with  the  cash  so  obtained  paying  wages  (C„)  to  work- 
men who  spend  it  (Nc)  among  other  tradesmen  who  redeposit 
it  in  banks  (C^).  These  three  types  are  not  the  only  ones,  but 
they  are  so  much  more  important  than  any  others  that  they 
merit  our  undivided  attention  before  a  completer  study  is 
undertaken.  Figure  18  has  been  constructed  for  the  purpose 
of  exhibiting  them  uncomphcated  by  other  details. 


Fig.  18. 

It  will  be  noted  that  not  all  of  the  flows  described  are  ex- 
amples of  the  circulation  of  money.  As  already  indicated, 
money  may  be  said  to  circulate  only  when  it  passes  in  ex- 
change for  goods.  Its  entrance  into  and  exit  from  banks  is  a 
flow,  but  not  a  circulation  against  goods.  In  the  diagram 
the  horizontal  arrows  represent  such  mere  banking  operations, 
not  true  circulation.  On  the  other  hand,  the  arrows  along  the 
sides  of  the  triangle  represent  actual  circulation.  The  dia- 
gram shows  four  such  arrows,  representing  the  four  chief 
types  of  circulation:    Oc  payments  of  money  from  "Other 


454        THE    PURCHASING    POWER   OF   MONEY     IAppend.  XII 

depositors"  to  "Commercial  depositors"  in  the  purchase  of 
goods;  On  payments  from  "Other  depositors"  to  "Non- 
depositors,"  as  when  a  housewife  pays  wages;  C„  payments 
from  "Commercial  depositors"  to  "Nondepositors,"  as 
when  a  firm  pays  wages;  and  Nc  payments  from  "Non- 
depositors"  to  "Commercial  depositors,"  as  when  a  wage 
earner  buys  goods  of  a  merchant. 

These  four  types  of  circulation  of  money  occur  in  the  three 
circuits  already  described,  being  sandwiched  between  the  flows 
from  and  to  the  banks.  The  first,  Oc,  is  contained  within 
the  circuit  BoOcC^,  and,  since  no  "Nondepositors"  inter- 
vene, represents  money  changing  hands  once  between  its  with- 
drawal from  bank  and  its  re-deposit  there.  The  remaining 
types  {On,  Cn,  and  Nc)  are  contained  within  the  two  other 
circuits  {BjOnNcC^  and  BcCnNcCf,),  and,  owing  to  the  fact 
that  "Nondepositors"  intervene,  represent  money  circulat- 
ing twice  between  withdrawal  and  re-deposit. 

In  short,  one  of  the  three  circuits  {BoOjC^)  shows  money 
circulating  once  out  of  bank.  Both  the  others  pass  through 
N,  and  show  money  circulating  twice  out  of  bank.  The 
diagram,  then,  represents  all  circulating  money  as  springing 
from  and  returning  to  the  banks;  all  of  it  as  circulating  at 
least  once  in  the  interim;  and  that  portion  handled  by  "Non- 
depositors"  as  circulating  once  in  addition.  Therefore,  the 
total  circulation  exceeds  the  total  flow  from  and  to  banks 
by  the  amount  flowing  through  "Nondepositors."  In  other 
words,  the  total  circulation  in  the  diagram  is  simply  the  sum 
of  the  annual  money  flowing  from  and  to  banks  and  the 
money  handled  by  "Nondepositors."  The  quotient  of  this 
sum  divided  by  the  amount  of  money  in  circulation  will  give 
approximately  the  velocity  of  circulation  of  money. 

II.    The  Complete  Formula 

We  have,  however,  still  to  consider  the  correction  to  be 
made  for  the  less  important  forms  of  monetary  circulation 
excluded  from  Figure  18. 


Sec.  6]  APPENDIX  TO   CHAPTER   XII  455 

In  order  to  estimate  the  degree  of  accuracy  of  the  first 
approximation  just  made  for  the  circulation  of  money,  we 
need  to  compare  this  approximation  with  a  complete  formula 
framed  to  include  all  possible  transfers  of  money  against 
goods.'  There  are  nine  possible  kinds  of  transfers,  three 
being  respectively  within  each  one  of  the  three  groups  C,  0, 
and  N,  and  six  being  between  each  pair  of  these  three,  in  either 
direction. 

The  exchanges  possible  within  a  class  are  (1)  those  between 
one  "Commercial  depositor "  and  another  "Commercial 
depositor";  (2)  those  between  one  "Other  depositor"  and 
another;  and  (3)  those  between  one  "Nondepositor  "  and 
another.  The  transfers  possible  between  classes  are  (4 
and  5)  those  between  "Commercial  depositors"  and  "Other 
depositors "  in  either  direction ;  (6  and  7)  those  between 
"  Other  depositors  "  and  "  Nondepositors  "  in  either  direction; 
and  (8  and  9)  those  between  "Nondepositors"  and  "Com- 
mercial depositors"  in  either  direction.  Thus  there  are 
three  intraclass  kinds  and  six  interclass  kinds  of  transfers  of 
money  against  goods. 

Figure  19  gives  a  complete  picture  of  all  these  nine  flows 
of  money  in  exchange  for  goods;  that  is,  of  the  entire  "cir- 
culation of  money."  The  nine  flows  are  represented  in  the 
diagram  by  the  nine  arrows  about  the  triangle,  six  being  along 
the  three  sides  of  the  triangle  and  representing  interclass 
circulation,  and  three  (c,  o,  and  n)  at  the  corners  to  represent 
intraclass  circulation.  The  remaining  six  arrows  on  the  hori- 
zontal lines  represent,  of  course,  mere  banking  operations. 
The  total  circulation  or  monetary  flow  (F)  in  exchange  for 

^  That  is,  all  transfers  within  the  community  considered.  If  it 
is  desired  to  include  as  part  of  a  community's  circulation  the  sums 
exported  or  imported  in  foreign  trade,  these  may  most  conveniently 
be  added  at  the  end.  But  even  if  they  be  included,  they  will  be  of 
trifling  significance,  partly  because  foreign  trade  is  usually  very 
small  compared  with  domestic,  and  partly  because  money  is  so  little 
used  in  foreign  trade,  especially  if  we  exclude  bullion  from  the 
category  of  money. 


456       THE   PURCHASING   POWER   OF  MONEY     [Append.  XH 

goods  is,  therefore,  the  sum  of  the  magnitudes  represented 
by  these  nine  arrows,  viz. 


F  =  Oc-\-Co^-Nc^-Cn  +  On  +  No  +  c  +  o-\-n. 


(1) 


This  is  an  exact  formula  for  the  circulation  of  money.     We 
shall  now  compare  it  with  the  inexact  first  approximation, 


Qi 


'3 


a 


Fig.  19. 


namely,  "money  deposited  plus  expenditures  of  'Nondeposi- 
tors. '"  This  comparison  will  express  the  error  of  the  first 
approximation,  and  will  suggest  a  method  of  transforming  the 
exact  formula  (1)  into  a  shape  more  suitable  for  statistical 
application.  First,  we  need  to  express  algebraically  the 
first  approximation.  This  may  easily  be  done  by  inspect- 
ing Figure  19.  The  total  money  deposited  is  0^  +  06  + 
Nj,  while  the  total  expenditure  of  "  Nondepositors "  is 
Nc  +  No.  The  sum  of  these  two  expressions  we  shall  call  ¥'. 
It  is:  — 

/^'  =  C,  +  0,+Ar,  +  iV,  +  iV„  (2) 


Sec.  6]  APPENDIX  TO   CHAPTER   XII  457 

which  is,  therefore,  the  algebraic  expression  for  the  first  ap- 
proximation. 

To  obtain  the  difference,  F  —  F',  between  the  exact  and  the 
approximate  formula,  we  subtract  (2)  from  (1),  canceling  Ne 
and  No  and  placing  the  negative  terms  first.  We  thus  obtain 
for  a  remainder  (/•)  the  following :  — 

r=/r_/r'=  -c,-0,-N,+Oc-h  Co+Cn-{-On-\-c+o-\-n.    (3) 

That  the  value  oi  F  —  F'  is  small  may  be  seen  clearly  by 
transforming  (3) .  We  shall  transform  it  by  means  of  another 
equation  (4)  given  below.  In  order  to  derive  this  new  equa- 
tion (4),  we  shall  need  to  make  a  digression.  This  new  equa- 
tion is  merely  a  special  application  of  the  general  principle 
that  the  net  outflow  (i.e.  outflow  minus  inflow)  from  the  con- 
tents of  any  reservoir  must  equal  the  net  decrease  in  its  con- 
tents during  the  same  time,  or  (algebraically  expressed)  that 
the  net  outflow  (positive  or  negative)  plus  the  net  increase 
in  contents  (negative  or  positive)  must  be  zero.  We  m_ay 
apply  this  principle  to  any  reservoir  or  store  of  money,  but 
shall  here  find  it  most  helpful  to  apply  it  to  the  reservoir  of 
money  contained  among  the  "Commercial  depositors"  and 
"Nondepositors"  taken  together  as  one  grmip.  Let  us  desig- 
nate the  combination  of  these  two  as  the  "CN  group."  The 
total  outflow  indicated  in  the  diagram  from  this  "CN  group" 
is  evidently  C,,  +  C<,  +  A^j,  +  No,  and  the  total  inflow  Be  + 
Oc  -\-  Bn  -\-  On-  Hence,  the  net  outflow,  so  far  as  the  diagram 
shows  us,  is  :  — 

C,-hCo  +  N,  +  No-Bc-Oc-Br,-On. 

This,  plus  the  net  outflow  not  shown  in  the  diagram,  is  the 
true  net  outflow.  Since  the  diagram  was  constructed  to  show 
only  flows  against  goods  (monetary  circulation),  and  flows  to 
or  from  banks,  we  have  still  to  take  account  of  money  flow- 
ing in  the  community  in  exchange  for  something  else  than 
goods,  and  that  flowing  without  any  exchange  at  all,  as  well 
as  any  net  outflow  outside  of  the  community. 

We  have  thus  to  take  account  of  three  undiagramed  flows. 


458       THE   PURCHASING   POWER  OF  MONEY     [Append.  XII 

The  first  is  the  net  outflow  of  money  from  the  '^CN  group  "  to 
the  "  0  group,"  which,  though  in  exchange,  is  not  in  exchange 
for  goods.  This  means  simply  cashed  checks,  for,  according 
to  the  classification  we  are  here  using,  "goods"  are  taken  to 
include  anything  exchangeable,  not  either  money  or  checks. 
Our  first  correction  is,  therefore,  the  net  outflow  of  money  from 
the  ^^CN  group"  for  cashing  checks,  i.e.  the  difference  be- 
tween the  checks  cashed  by  the  '^CN  group"  for  the  "0 
group  "  and  those  cashed  in  the  opposite  direction. 

It  will  be  understood  that  we  have  nothing  to  do  here  with 
the  cashing  of  checks  at  banks,  for  this  is  included  in  the  dia- 
gram {Bo,  Bn,  and  B^.  Moreover,  we  have  nothing  to  do 
here  with  cashing  of  checks  within  the  "CAT  group,"  as  when 
a  storekeeper  cashes  a  check  presented  by  a  "Nondepositor." 
We  have  only  to  do  with  the  net  outflow  for  cashed  checks 
from  CN  to  0.  This  net  outflow  (which  may  be  positive, 
negative,  or  zero)  we  shall  designate  by  the  letter  a,  to  stand 
for  "accommodation"  checks. 

For  the  second  correction,  we  have  to  designate  the  net  out- 
flow of  money  given  away  by  the  "CN  group"  in  gifts,  taxes, 
thefts,  etc.,  for  which  no  speciflc  goods  are  received  in  return. 
This  net  outflow  may  be  designated  by  g. 

We  have,  thirdly  and  lastly,  the  net  outflow  of  money  with 
respect  to  the  "CN  group"  outside  of  the  community,  i.e.  the 
net  amount  of  money  which  is  lost  to  the  country  by  export, 
fire,  shipwreck,  melting,  etc.,  in  excess  of  that  imported, 
minted,  etc.  This  net  outflow  may  be  designated  by  e,  to 
stand  for  "external"  outflow.  Adding  the  net  undiagramed 
outflow  (a  -{-  g  -{■  e)  to  the  net  diagramed  outflow,  we  have, 
for  the  total  net  outflow, 

C,  +  Co  +  N,  +  No-  Bc-Oc-  Bn-On  +  a  +  g-\-e. 

Now,  on  the  reservoir  principle  already  explained,  the  alge- 
braic sum  of  this  net  outflow  from  the  "CN  group"  and  the 
net  increase  of  the  money  in  that  group  must  be  zero.  That 
is,  representing  this  net  increase  by  i,  we  have 

0=C,  +  Co  +  N,-{-N,-B-O,-Bn-0n-{-a-{-g-{-e-{-i.  (4) 


Sec.  6]  APPENDIX  TO   CHAPTER   XII  459 

We  now  place  this  new  equation  (4)  under  the  old  equation  (3), 
giving  the  value  of  r  =  F  —  F'  in  the  following  manner :  — 

r  =  -  (Cb)  -Ob-  {Nb)  +  (Oc)  +  Co+Cn+  iOn)]+c  +  o+n 

0=      (Cb)  +  Co+{Nb)  +  No-Bc-{Oc)-Bn         ~{On)  +  a  +  g  +  e  +  i. 

Adding  and  canceling  the  terms  of  (3)  and  (4)  indicated  in 
parentheses,  and  rearranging  the  remaining  terms,  we  have 

r  =  F-F'=  (Co-\-Cn-  B,)-\-  (Co  +  No  -  Ob)  +  {c  +  o 
+  n)  +  (a-\-g  +  e)-\-i-Bn.  (3)' 

The  letters  are  grouped  in  parentheses  forming  six  terms, 
arranged,  as  far  as  can  be  judged,  in  the  order  of  descending 
importance. 

By  using  the  expression  just  obtained  for  r,  the  complete 
formula  (1)  for  the  circulation  of  money  may  now  be  put  in  a 
form  suitable  for  statistical  application.  Since  r  =  F  —  F', 
then  F  =  F'  -\-  r.  Substituting  for  F'  and  r  the  expression 
already  given  in  equations  (2)  and  (3)',  we  have,  as  a  trans- 
formation of  (1), 
F  =  F'  -\-r 

=-{Cb  +  Ob-^Nb)  +  {Nc-VNo) 

+  (a  +  Cn-5,)  +  (C<,  +  Ar„-0,)  +  (c  +  o  +  n)  +  (o  +  g 
+  e)  +  ^•  -  5„  (1)' 

=  (1)  all  money  deposited 

+  (2)  money  expenditures  of  "  Nondepositors  " 

+  (3)  Cs  money  expenditures  from  tills  {i.e.  money  expendi- 
tures in  excess  of  money  withdrawn  from  bank) 

+  (4)  O's  money  receipts  pocketed  {i.e.  money  receipts  in 
excess  of  money  deposited  in  bank) 

-|-  (5)  intraclass  monetary  circulation 

+  (6)  CN'^  undiagramed  net  outflow  of  money 

-f  (7)  CN'b  net  increase  of  money  on  hand 

—  (8)  iV's  withdrawals  of  money  from  bank. 

This  is  a  complete  and  universal  formula  for  the  circu- 
lation of  money  in  any  community.     Its  first  two  terms 


460       THE   PURCHASING   POWER  OF  MONEY     [Append.  XII 

constitute  the  first  approximation,  and  the  other  six 
terms  constitute  r,  which  may  be  called  the  "remainder 
term." 

The  first  and  second  terms  are  by  far  the  most  important. 
The  last  three  terms  —  sixth,  seventh  and  eighth  —  are 
doubtless  quite  negligible  under  all  circumstances  actually 
met  with,  I  am  also  reasonably  confident  that,  in  the  United 
States,  the  3d,  4th,  and  5th  terms  amount  to  less  than  10  per 
cent  of  the  total  and  probably  less  than  5  per  cent.  There- 
fore, the  complete  omission  of  all  except  the  first  two  terms 
would  still  give  us  a  fairly  good  figure  for  the  total  F;  for 
any  one  familiar  with  the  inaccuracies  of  statistics  knows 
that  5  or  10  per  cent  is  a  small  error,  especially  for  a 
magnitude  which  has  hitherto  eluded  any  attempt  at  meas- 
urement. 

We  may,  therefore,  distinguish  three  successive  stages  in  our 
approximations.  The  first  approximation  comprises  only 
the  first  two  terms,  viz.  money  deposited  plus  expenditures 
of  "  Nondepositors  "  ;  the  second  includes,  in  addition,  terms 
(3),  (4),  and  (5),  viz.  till-paid  money  expenditures  of  C,  pock- 
eted money  receipts  of  0,  and  intraclass  circulation;  while 
the  third  is  rendered  absolutely  complete  by  including  terms 
(6),  (7),  and  (8),  none  of  which  has  practical  importance. 
The  complete  formula  is  presented  in  the  hope  of  arousing 
discussion  and  investigation  which  will  disclose  in  particular 
to  what  extent  it  may  be  applied  in  countries  where  data 
exist  for  the  first  two  terms,  viz.  money  deposited  and  expend- 
itures of  "  Nondepositors."  The  former  is  to  a  large  extent 
a  matter  of  daily  record  in  most  civilized  countries,  and  the 
latter  consists  chiefly  of  wages,  a  magnitude  which  has  for 
long  been  a  favorite  subject  for  statistical  estimate. 

§  7  (to  Chapter  XII,  §  4) 
Application  of  Formula  to  Calculation  of  V  for  1896  and  1909 

We  shall  now  exemplify  the  use  of  our  formula  by  means  of 
actual  figures  for  the  United  States.      The  Report  of  the 


Sec.  7]  APPENDIX  TO    CHAPTER   XII  461 

Comptroller  of  the  Currency  for  1896,  already  referred  to, 
and  the  special  report  of  the  National  Monetary  Commission 
for  1909,  give  a  basis  for  estimating  the  first  term  (Cs  +  O*  + 
Nb),  the  annual  money  deposited  in  banks  in  those  years. 
Both  reports  were  made  under  the  direction  of  Professor 
David  Kinley  of  the  University  of  Illinois.  We  shall  consider 
first  the  figures  for  1896.  The  total  money  deposited  in 
banks  on  the  settling  day  nearest  July  1, 1896,  was  7.4  per  cent 
of  the  total  deposits  of  all  kinds.  This  total  for  all  reporting 
banks  was  303  millions,  of  which  7.4  per  cent  would  make 
$22,400,000.  It  was  made  up  of  over  $16,200,000  from  3474 
national  banks,  and  the  remainder  from  2056  other  banks. 
There  were,  all  together,  according  to  the  Comptroller's  Re- 
port, about  13,000  banks  in  the  country  at  that  time.  On  the 
basis  of  these  figures,  the  Comptroller  attempts  to  estimate 
the  (retail)  deposits  of  all  kinds  for  all  these  13,000  banks, 
assuming  that  the  average  deposit  was  the  same  as  for  the 
country  banks  replying.  This  average  was  $2375  for 
banks  in  places  of  12,000  inhabitants  or  less.  Applying 
this  average  to  the  unreporting  banks,  we  would  increase 
the  retail  deposits  (which  were  $26,500,000)  by  an  addi- 
tional $17,800,000. 

If  we  assume  the  same  ratio  of  increase  for  the  total  money 
deposits,  the  sum  of  22.4  millions  would  be  increased  by  15.0 
millions,  making  a  total  of  37.4  millions,  as  the  amount  of 
money  deposited  in  banks  on  the  settling  day  nearest  July  1, 
1896.  This  figure  represents  at  least  a  rough  approximation 
to  the  inflow  of  cash  into,  and,  therefore,  also  the  outflow  of 
cash  from,  the  banks  of  the  country.  Multiplying  by  305 
settling  days  for  the  year,  we  obtain  11.4  ])illions  as  the 
total  annual  amounts  deposited.  The  figures,  being  for  the 
settling  day  nearest  the  first  of  July,  are  probably  above 
the  daily  average  for  the  year.  Thus  11.4  is  an  upper  limit 
rather  than  an  estimate.  Later  we  shall  also  set  a  lower 
limit. 

The  preceding  figures  relate  to  the  year  1896.  Similar 
calculations  for  1909  have  been  made  by  Professor  David 


462       THE    PURCHASING   POWER   OF  MONEY     [Append.  XII 

Kinley  ^  with  the  assistance  of  Professor  Weston.  The  re- 
sulting figure  for  money  deposited  in  1909  is  19.1  billions. ^ 

But  if  it  is  necessary  to  adjust  the  figures  for  deposits  of 
checks  in  1896  and  1909  because  the  days  selected  are  excep- 
tional (see  §  4  of  this  Appendix) ,  it  is  also  necessary  to 
adjust  the  figures  for  the  deposits  of  money.  On  July  1, 1896, 
many  June  bills  must  have  been  paid  by  cash  as  well  as  by 
check  and  on  March  16,  1909,  the  middle  of  a  month,  there 
must  have  been  slackness  of  settlements  by  cash  as  well  as 
by  check.  Consequently,  like  the  total  deposits  of  checks, 
the  total  deposits  of  money  made  on  July  1, 1896,  were  in  all 
probability  above  the  daily  average  for  1896,  and  on  March 
16,  1909,  they  were  below  the  daily  average  for  1909.  In 
other  words,  without  adjustment  for  the  abnormality  of  the 
days  selected,  the  figure  expressing  monetary  circulation  for 
1896  would  be  too  large,  and  that  for  1909,  too  small.  That 
is,  without  such  adjustment  our  calculations  merely  set  an 
upper  limit  in  1896  and  a  lower  limit  in  1909. 

But  we  may  easily  set  the  opposite  limits.  We  may  be 
reasonably  sure  that  deviations  from  the  average  are  less 
for  money  deposits  than  for  check  deposits.  It  cannot  be 
expected  that  daily  money  deposits  fluctuate  as  greatly  as 

'  See  "Note  on  Professor  Fisher's  Formula  for  Estimated  Velocity 
of  Circulation  of  Money."  Publications  American  Statistical  Asso- 
ciation, March,  1910.  The  calculations  are  based  on  data  taken  from 
Professor  Kinley's  valuable  monograph  on  "  Credit  Instruments," 
61st  Congress,  2d  Session,  Doc.  No.  399  in  Reports  of  National 
Monetary  Commission. 

2  Professor  Kinley  gives  18.3.  The  difference  is  due  to  the  fact 
that  Professor  Kinley,  while  estimating  the  daily  deposits  as  62.9 
millions,  calls  this  in  round  numbers  60  millions.  It  seems  prefer- 
able to  use  the  estimate  as  it  stands  and  make  any  allowances  for 
errors  at  the  end  rather  than  the  beginning.  Professor  Kinley  also 
takes  305  settling  days  for  the  year,  this  being  the  number  used  by 
Professor  Kem merer  for  1896.  But  Mr.  Gilpin  of  the  New  York 
clearing  house  tells  me  that  the  clearing  house  business  days,  though 
305  in  1896,  were  303  in  1909.  I  have  therefore  used  303  as  the 
number  of  settling  days  in  1909.  The  product  62.9  millions,  times 
303,  is  19.1  biUions. 


Sec.  7]  APPENDIX  TO   CHAPTER   XII  463 

daily  check  deposits.  Practically  all  check  payments  are  in- 
fluenced by  the  periodicity  in  receipts  of  checks  by  the  de- 
positors (as  of  their  salary,  interest,  or  dividend  checks) ,  or  by 
the  periodicity  of  credit  extended  to  them  (as  of  the  trades- 
men who  render  them  monthly  bills) .  While  the  fluctuations 
to  which  money  payments  are  subject  are  more  or  less  similar, 
they  are  much  less  in  extent  for  two  reasons :  First,  the  pay- 
ment or  credit  cycles  which  influence  the  fluctuations  of 
money  deposits  are  usually  shorter  than  those  which  influence 
the  fluctuations  of  check  deposits ;  the  wage  earner  usually 
gets  his  money  weekly  as  against  the  salaried  man  who  re- 
ceives his  check  monthly,  or  the  stockholder  who  receives 
his  dividends  quarterly.  Secondly,  unlike  check  payments, 
many,  if  not  most,  money  payments  have  no  payment  or  credit 
cycle.  There  is  no  credit  cycle  in  what  are  called  "cash" 
payments,  for  they  imply  that  no  credit  is  given.  The  receipts 
at  "cash  stores,"  the  smaller  receipts  at  all  stores,  the  receipts 
of  tramway,  railway,  and  steamship  oflices,  the  receipts  at 
theaters  and  many  miscellaneous  establishments  are  almost 
wholly  on  a  cash  basis  and  result  in  daily  and  fairly  steady 
money  deposits  made  by  these  establishments.  These  are 
facts  of  every-day  experience  and  are  confirmed  by  inquiry  of 
bankers,  who  state  that  their  money  deposits  are  far  steadier 
day  by  day  than  their  check  deposits.  Confirmatory  and 
conclusive  evidence  is  also  obtainable  from  Kinley's  investi- 
gation in  the  Comptroller's  Report  for  1896  (p.  95).  If  check 
and  money  deposits  were  to  fluctuate  in  perfect  sympathy 
with  each  other,  the  percentage  of  the  total  which  consists  of 
checks  would  remain  constant.  But  if,  as  we  shall  endeavor 
to  show,  the  excess  or  abnormality  of  check  deposits  on  July  1 
is  greater  than  the  excess  or  abnormality  of  money  deposits 
on  that  date,  then  we  ought  to  find  that  the  percentage  of 
check  deposits  is  greater  on  July  1  than  usual.  The  figures 
of  the  Comptroller's  Report  indicate  that  this  is  the  case. 
They  show  that  the  percentage  of  checks  received  (unfortu- 
nately not  quite  synonjonous  with  "deposits")  was  on 
September  17,  1890,  91.0  per  cent  and  on  July  1  of  the  same 


464       THE   PURCHASING   POWER   OF  MONEY     [Append.  Xil 

year,  92.5  per  cent,  or  1^  per  cent  higher.  Again,  com- 
paring July  1, 1896,  with  the  nearest  available  date  for  another 
season  of  the  year,  namely,  September  15,  1892,  we  find  the 
figures  to  be  as  follows:  for  September  15,  1892,  check  re- 
ceipts, 90.6  per  cent;  for  July  1,  1896,  check  deposits,  92.5 
per  cent,  or  1.9  per  cent  higher.  The  excess  would  have  been 
still  greater  if  both  the  figures  were  for  receipts  instead  of  one 
of  them  being  for  deposits;  for,  as  the  Comptroller  says,  the 
inclusion  of  other  receipts  than  deposits  tends  to  exaggerate 
the  percentage  of  checks.  That  July  1  has  a  far  larger  pro- 
portion of  checks  than  June  30  is  indicated  by  the  figures  for 
retail  deposits  for  June  30, 1894,  and  July  1,  1896,  the  former 
being  58.5  per  cent  and  the  latter  67.6  per  cent,  or  9.1  per 
cent  higher.  We  should  be  cautious,  however,  in  drawing  any 
quantitative  conclusion  from  this  difference,  since  the  investi- 
gations for  1894  and  1896  were  conducted  somewhat  differ- 
ently. But  the  difference,  as  we  find  it,  harmonizes  with  all 
the  facts  at  hand.  Similar  confirmation  may  be  drawn  from 
the  absence  of  any  contrast  between  the  figures  for  June  30 
and  September  17,  1881,  as  compared  with  the"  sharp  contrast 
already  noted  between  July  1  and  September  17,  1890.  The 
credit  receipts  in  1881  on  June  30  and  September  17  were 
91.77  per  cent  and  91.85  per  cent,  respectively,  which  figures 
are  substantially  equal,  while,  as  above  noted,  for  July  1  and 
September  17,  1890,  we  find  a  difference  of  1|-  per  cent. 

We  feel,  therefore,  safe  in  concluding  that  check  deposits 
are  subject  to  greater  fluctuations  or  abnormalities  than 
money  deposits.  Consequently  the  deposits  of  money  on 
July  1,  1896,  while  they  may  have  exceeded  the  daily  aver- 
age, were  probably  not  so  far  above  the  daily  average  as 
were  the  deposits  of  checks;  also  on  March  16,  1909,  the 
deposits  of  money  were  probably  not  so  far  below  the 
average  daily  deposits  of  money  as  were  the  deposits  of 
checks. 

Now,  if  this  were  not  true,  —  if  the  money  deposits  fluctu- 
ated exactly  parallel  with  check  deposits,  —  we  should  need  to 
assume  the  same  correction-factors  for  money  as  for  checks, 


Sec.  7] 


APPENDIX   TO    CHAPTER   XII 


465 


viz.  .68  in  1896  and  1.17  in  1909,  with  the  results  given  in 
column  (1)  of  the  following  table:  — 


Estimated  Money  Deposits  of  Yeab 

(1) 

(2) 

Monet  De- 
posited ON  Day 
Selected 
(In  Millions) 

(3) 

Assuming  Day 

AN  Average  One 

(In  Billions) 

(4) 
Assuming  Cor- 
rection Factors 
equal  to   those 
FOB  Check 
Deposits 

(5) 

Mean   between 

Two  Preceding 

Columns 

1896    .     . 
1909    .     . 

37.4 
62.9 

11.4 
19.1 

7.8 

22.3 

9.6 
20.7 

We  see  that  the  true  value  of  the  money  deposited  in  banks 
in  1896  must  in  all  probability  lie  between  7.8  and  11.4  bilUons, 
and  in  1909,  between  19.1  and  22.3  billions.  If,  in  each  case, 
we  split  the  difference,  the  estimates  become  for  1896,  9.6, 
and  for  1909,  20.7.  The  truth  cannot  be  far  from  these 
figures,  for  there  are  only  narrow  hmits  on  either  side.  The 
probable  error,  judged  roughly  from  the  calculated  limits  and 
from  the  character  of  the  estimates  of  these  limits,  is  placed 
at  about  1  billion  in  each  case.  It  will  be  noted,  of  course, 
that  this  error  is  larger  proportionally  in  1896  than  in  1909. 

We  have  now  estimated  the  first  term  (total  deposits)  of  the 
formula  for  the  total  circulation  of  money. 

The  next  term  (Nc+Ng)  is  the  expenditure  of  the  "Non- 
depositors"  made  to  other  classes.  This  is  practically  the 
expenditure  of  wage  earners.  The  Census  gives  the  average 
wages  in  manufacturing  industries  as  $430.  Mr.  William  C. 
Hunt  of  the  Census  Bureau,  in  an  unofficial  memorandum 
which  he  has  kindly  allowed  me  to  see,  has  estimated  that  the 
laborers  in  the  United  States  number  about  18,400,000.  Let 
us  assume,  as  a  reasonable  approximation,  that  their  average 
wages  are  the  same  as  the  average  in  manufacturing  industries, 
namely,  $430.  We  first  apply  this  to  the  8.5  millions  of  people 
which  Mr.  Hunt  estimates  are  engaged  in  manufacturing  and 
mechanical  pursuits  and  trade  and  transportation.  These 
2h 


466       THE   PURCHASING   POWER  OP  MONEY     [Append.  XII 

persons,  therefore,  receive  about  3.7  billions  of  dollars  in 
wages. 

The  remaining  classes  of  laborers  are  domestic  servants  and 
agricultural  laborers.  These,  however,  receive  board  and 
lodging  as  part  pay.  Since  food  and  rent  form  about  60  per- 
cent of  workingmen's  budgets,  we  may  assume  that  the  actual 
money  paid  to  domestic  and  agricultural  workers  is  only  about 
40  per  cent  of  that  paid  to  manufacturing  laborers,  i.e.  about 
$170.  Mr.  Hunt  estimates  the  number  of  domestic  and  agri- 
cultural laborers  at  9.9  millions.  Hence  the  total  money 
they  handle  in  a  year  is  probably  about  1.7  billions.  This, 
added  to  the  previous  3.7  bilhons,  gives  5.4  billions  as  the  to- 
tal money  paid  in  wages  in  the  United  States  All  these 
figures  relate  to  the  year  1900,  while  the  figures  for  our  first 
term  relate  to  1896.  In  the  interim  both  the  number  of 
laborers  and  their  wages  doubtless  increased  somewhat  and 
we  must,  therefore,  make  a  correction  for  each.  We  shall  as- 
sume that  the  number  of  laborers  increased  in  the  same  ratio 
as  population,  and  that  population  increased  between  1896 
and  1900  at  the  same  rate  per  annum  as  between  1890  and 
1900.  This  would  reduce  the  5.4  bilhons  to  5.0  billions. 
If,  instead  of  population,  we  use  the  number  of  employees  in 
manufacturing  and  mechanical  pursuits  as  given  by  the 
Bureau  of  Labor,^  the  result  is  lower,  viz.  4.6.  The  truth  prob- 
ably lies  between,  since  agricultural  labor,  for  which  we 
have  no  statistics,  has  probably  not  increased  as  fast  as 
manufacturing  labor,  and,  therefore,  even  if  labor  as  a  whole 
increased  in  the  same  ratio  as  population,  the  relative  in- 
crease of  manufacturing  labor,  as  compared  with  agricultural 
labor,  would  mean  a  greater  payment  of  money  wages.  We 
may  select  4.8  billions  as  close  to  the  truth.  As  to  the  rate  of 
wages,  the  index  numbers  of  the  Bureau  of  Labor  ^  for  1896 
and  1900  are  99.5  and  104.1  respectively.  On  this  account, 
therefore,  we  should  still  further  reduce  our  estimate  of  money 

1  Bulletin  of  the  Bureau  oj  Labor,  No.  77,  July,  1908,  p.  7. 
» Ibid.,  p.  7. 


Sec.  7]  APPENDIX  TO   CHAPTER   XII  467 

wages  paid  in  1896,  —  in  the  ratio  of  104.1  to  99.5  or  from 
4.8  billions  to  4.6  billions.  Furthermore,  a  small  fraction 
of  these  laborers  are  prosperous  enough  to  have  bank  ac- 
counts, and  the  expenditures  of  these  should  not  be  included 
among  the  expenditures  of  "Nondepositors."  About  4^  bil- 
lions is  probably  as  close  to  the  truth  as  we  can  expect  to  get. 

But  we  must  now  add  to  this  an  allowance  for  "  Nondeposi- 
tors  "  other  than  wage  earners.  Some  of  the  2.1  milUon  clerks 
and  8.6  miUion  proprietors  and  professional  men  in  Mr. 
Hunt's  estimates,  though  not  laborers,  are  nevertheless 
"Nondepositors."  As  to  the  clerks,  it  is  said  by  business 
men  that  most  clerks  who  receive  over  $100  a  month,  and 
some  who  receive  less,  have  bank  accounts.  Probably,  the 
great  bulk  of  the  2  millions  of  persons  estimated  as  clerks 
are  far  below  $100  a  month,  and  many  are  doubtless  included 
who,  like  office  boys,  have  less  than  what  are  ordinarily 
called  wages.  To  make  a  guess  sure  to  be  large  enough,  let  us 
say  that  three-fourths  of  the  clerks  have  no  bank  account  and 
average  $60  a  month.  Even  then  the  total  cash-paid  clerk  hire 
would  scarcely  exceed  a  billion. 

Among  the  proprietors  and  professional  men,  the  only 
group  we  need  to  consider  is  agricultural  proprietors  (5.7 
millions).  The  remainder  consists  of  classes  among  which 
bank  accounts  are  practically  universal.  Of  these  agricul- 
tural proprietors,  those  who  have  no  bank  accounts  are  doubt- 
less smaller  ones,  living  in  districts  where  little  money  changes 
hands.  Their  number  could  certainly  not  exceed  four  mil- 
lions, which  would  be  over  two  thirds  of  the  whole.  The  prob- 
lem is,  What  cash  do  these  farmers  pay  to  depositors,  com- 
mercial and  other  ?  Practically,  this  means,  What  do  they 
pay  to  country  storekeepers  ?  Their  payments  to  laborers  or 
other  farmers  are  payments  to  other  "  Nondepositors  "  and  do 
not  concern  us  here.  For  rent,  food,  or  such  farm  supplies 
as  they  can  raise  themselves,  they  pay  little  or  nothing. 
Thus,  the  hay  crop  of  the  nation  is  said  to  exceed  in  value  the 
wheat  crop;  but  so  little  hay  is  marketed  that  it  is  seldom 
quoted  or  thought  of  as  a  market  commodity.     Even  the 


468       THE    PURCHASING   POWER  OF  MONEY     [Append.  XII 

trade  of  these  farmers  with  the  storekeeper  is  conducted 
largely  by  barter  or  book  credit.  Their  expenditures  in  actual 
money  may  be  conjectured  to  average  less  than  S250  a  year 
for  each  farmer,  making  less  than  a  billion  dollars  at  most 
(even  if  the  number  of  such  farmers  be  counted  at  4 
millions). 

It  seems  safe  to  say,  then,  after  allowing  a  billion  for  clerks 
and  a  billion  for  farmers,  that  the  total  expenditures  of 
"  Nondepositors  "  cannot  exceed  4^  +  1+1  =  Q^  billions. 

On  the  other  hand,  it  can  scarcely  be  less  than  5  billions. 
To  reduce  it  to  this  figure  would  require  us  practically  to  ig- 
nore the  existence  of  "  Nondepositors "  other  than  wage 
earners,  or  to  assume  a  large  error  in  the  estimate  of  wages. 

We  conclude  that  for  1896  the  second  term  lies  somewhere 
between  5  and  6^  billions.  Placing  it  midway,  we  obtain  ap- 
proximately 5.7  billions  with  a  possible  error  of  .7  or.  8.  Sim- 
ilar calculations  for  1909  show  13.1  billions  for  the  second 
term  with  a  possible  error  of  1.0.  To  quote  from  Professor 
Kinley's  article  already  referred  to :  ^  — 

"  The  second  term  of  the  formula  is  the  money  payments  of 
*  Nondepositors,'  made  up  principally,  as  Professor  Fisher 
thinks,  of  the  wages  of  working  people.  The  following  table 
shows  an  estimate  of  the  increase  from  1900  to  1909  in  certain 
pursuits  on  the  basis  of  the  percentage  of  increase  from  1890 
to  1900  and  on  census  and  railroad  returns  since  1900.  As 
far  as  possible  salaried  officers  are  eliminated. 

Increase  Estimate 

1890             1900          Per  1909 
Cent 

Agricultural  pursuits     .      8,565,926    10,381,765    21.2  12,362,605 
Domestic    and    personal 

service      ....      4,220,812      5,580,657    32.2  7,377,628 

Total 19,740,233 

Trade    and    transporta- 
tion     .....      1,977,491      2,617,479    35.2  4,275,913 
Manufacturing           and 

mechanism    .     .     .      4,251,613      5,208,406  6,935,113 

Total 11,211,026 

*  Publications  of  the  American  Statistical  Association,  March,  1910, 


Sec.  7]  APPENDIX  TO   CHAPTER   XII  469 

"A  rough  calculation  based  on  the  figures  of  Census  BuU 
letin  No.  93  gives  us  about  $550  as  the  average  yearly  wages 
of  people  in  manufacturing.  If  we  should  include  mechani- 
cal pursuits,  probably  the  average  should  be  raised  a  little. 
Very  likely  $600  would  be  more  nearly  correct  for  this  class. 

"Again  the  Report  of  the  Interstate  Commerce  Commission 
for  1907  gives  figures  from  which  it  appears  that  the  average 
yearly  wage  is  about  $640.  It  is  more  difficult  to  get  a  ground 
for  making  an  estimate  of  the  money  wages  of  those  engaged 
in  agricultural  and  domestic  pursuits.  Doubtless  it  is  more 
than,  at  first  thought,  might  be  believed.  The  money  wages 
of  domestic  servants  at  present  probably  will  average  not  less 
than  $250  a  year.  Agricultural  laborers  are  certainly  receiv- 
ing a  good  deal  more  than  formerly,  and  $300  or  $350  probably 
will  not  be  too  large  a  sum  to  assign  to  these.  Accordingly,  we 
may  recapitulate  as  follows  :  — 

Trade  and  transportation         4.3  millions  at  $640  $2,752  millions 

Manufacturing    and    me- 
chanical pursuits        .        6.9  millions  at  $550  $3,790  millions 

Agricultural  pursuits   .     .      12.4  millions  at  $300  $3,720  millions 

Domestic  and  personal  ser- 
vice             7.4  millions  at  $250  $1,850  millions 

Clerks,     etc.,    having    no 

bank  account $1,000  millions 

Total $13,112  miUions 

"This  gives  us  the  second  term  of  the  formula." 
We  have  now  estimated  the  first  two  terms  (constituting 
together  what  has  been  called  the  first  approximation)  for 
both  1896  and  1909. 

To  this  first  approximation  must  be  added  the  remainder, 
r,  consisting  of  the  many  terms  already  explained,  most  of 
which  are  not  known  with  exactness,  but  all  of  which  are 
known  to  be  small.  The  term  "small"  is  always  relative, 
and  in  this  case  a  term  is  small  for  1896  which  is  small  com- 
pared to  16  bilhons.  For  instance,  160  millions  is  a  mere 
trifle,  being  only  1  per  cent  of  16  bilhons,  while  16  millions  is 
only  one  tenth  of  1  per  cent.  For  purposes  of  comparison 
we  do  not  need  exact  statistics  for  the  various  terms  of  which 


470       THE    PURCHASING    POWER  OF  MONEY     [Append.  XII 

r  is  composed.  All  we  need  to  know  is  that  r  is  small  and 
that  it  varies  approximately  as  the  rest  of  circulation  varies. 
Under  these  circumstances  a  large  mistake  in  estimating  it 
will  make  a  small  error  in  comparisons.  Only  in  case  r  were 
at  once  large  and  variable  relatively  to  the  other  terms  could 
a  mistake  in  its  estimation  greatly  affect  the  comparisons. 
Our  attempt  to  estimate  r  has  been  made,  not  so  much  for 
the  purpose  of  obtaining  its  absolute  value,  as  to  set  for  it 
wide  and  safe  limits. 

The  magnitude  r  consists  of  all  the  five  terms  of  our  for- 
mula beyond  the  second.     We  shall  take  these  up  in  order. 

The  third  term  of  the  formula  is  (Co  -\-  Cn  —  Be).  This 
represents  the  till-paid  commercial  expenditures,  or  the  excess 
of  the  money  paid  out  by  "Commercial  depositors"  over  the 
money  withdrawn  by  them  from  banks.  Personal  inquiry 
shows  that  the  great  bulk  of  the  money  withdrawn  by  "Com- 
mercial depositors"  from  the  banks  is  drawn  for  the  purpose 
of  paying  wages ;  also  that  the  great  bulk  of  the  actual  money 
expended  by  "Commercial  depositors"  is  expended  for  wages. 
In  other  words,  €„  is  very  small  compared  with  Cn,  and  the 
sum  of  the  two  is  nearly  the  same  as  Be.  Hence  the  difference 
{Co-hCn  —  Be),  or  till-paid  expenses,  is  nearly  zero.  Till- 
paid  expenses,  being  mostly  wages  and,  as  all  observation 
shows,  only  a  small  part  of  total  wages  {4:^  billions)  —  cer- 
tainly not  over  one  tenth  —  can  be  set  down  as  less  than  half 
a  billion  in  1896  and  less  than  a  billion  in  1909. 

The  fourth  term  (C^  -\-  No  —  Oj,)  is  O's  money  receipts 
which  are  pocketed  instead  of  being  deposited.  Now  O's 
money  receipts,  Cq-^No,  are  small  in  the  first  place,  for  0, 
being  depositors,  usually  receive  their  dividends,  interest, 
and  salaries  by  check.  The  chief  exception  is  found  in  the 
rents  and  the  professional  fees  paid  by  workingmen  to  land- 
lords, physicians,  etc.,  payments  which  constitute  most  of  No. 
But  these  rents  and  fees  paid  by  workingmen  to  private  indi- 
viduals are  only  a  part  of  total  rents  and  fees  of  workingmen, 
and  the  total  rents  and  fees  themselves  are  known  by  statistics 
of  workingmen's  budgets  to  be  only  about  20  per  cent  of 


Sec.  7]  APPENDIX  TO   CHAPTER   XII  471 

wages.  From  this  and  other  clews,  we  may  safely  set  half  a 
billion  as  an  upper  limit  for  the  fourth  term  in  1896.  Pro- 
fessor Kinley  places  .8  billion  as  the  upper  limit  in  1909. 

The  fifth  term  {c-\-  o-{-n)  is  the  circulation  within  each 
of  the  three  groups.  Obviously  only  in  trifling  cases  does 
money  circulate  between  one  "Commercial  depositor"  and 
another,  between  two  "Other  depositors,"  or  between  two 
"Nondepositors."  Half  a  billion  is  put  as  an  extreme  upper 
limit  for  the  total  for  1896  and  .8  by  Professor  Kinley  for  1909. 
This  would  mean  that  about  one  dollar  out  of  every  thirty-five 
expended  is  passed  on  to  other  persons  who  are  within  the  class 
to  which  the  expender  belongs.  In  fact,  the  universal  testi- 
mony of  such  few  representatives  of  c,  o,  and  n  as  I  have  been 
able  to  interrogate  personally  is  that  the  true  ratio  is  less  than 
this. 

The  remaining  three  terms  are  even  more  insignificant.  In 
the  normal  state  of  equiUbrium  for  the  "CN  group"  it  is  evi- 
dent that  the  sixth  and  seventh  terms  would  both  be  sub- 
stantially zero.  The  eighth  term,  withdrawals  from  banks 
by  people  who  have  no  bank  accounts,  represents  very  excep- 
tional conditions,  such  as  where  workmen  cash  checks  at 
banks.  Workmen  seldom  have  checks  to  cash  and,  when 
they  have,  usually  cash  them  in  stores  or  saloons. 

We  shall  summarize  the  estimates  for  each  of  the  eight 
terms  in  the  following  table.  Each  term  is  placed  midway 
between  upper  and  lower  limits  estimated  as  safe,  and  the 
possible  variation  in  either  direction  is  indicated  after  a  "  ±  ". 
Thus,  $300,000,000  ±  $300,000,000  means  simply  that,  though 
$300,000,000  is  assigned  as  the  estimate,  the  true  value 
may  be  more  or  less  by  an  amount  not  exceeding  S300,- 
000,000,  in  other  words,  that  the  truth  lies  between  $600,000,- 
000  and  zero.  Instead  of  half  billions  we  have  used  in  the 
table  $600,000,000  as  being  more  easily  divisible  by  two. 
The  results  for  both  years  are  given  in  the  following  table,  in 
which  generous  estimates  are  given  for  the  "probable  error" 
in  each  case.  In  fact  most  of  these  "probable"  errors  are 
improbably  large. 


472       THE    PURCHASING   POWER   OF  MONEY     [Append.  XII 


1896 


1909 


1.  Money  deposited    (Cs  +  Ob 

+  N) 

2.  Expenditure     of     "  Nonde- 

positors"    {Nc  +  A'',,)  •     . 

3.  C's  expenditure,   till  paid  . 

{Co  +  C„-  Be)   .     .     .     . 

4.  O's       receipts,        pocketed 

(Co  +No-Oh)  .     .     .     . 

5.  Intraclass    circulation    (  c  + 

0  +  n) 

6.  Net    undiagramed     outflow 

from  CN  (a  +  g  +  e) 

7.  Net  increase   of    money  of 

CN  (i)        

8.  Money       withdrawn      from 

banks     by     "Nondeposi- 
tors"  (  -  Bn)      .     .     .     . 


9.6  ±  1.5 

5.7  ±  .7 
0.3  ±  .3 
0.3  ±  .3 
0.3  ±  .3 
0.0  ±  .1 
0.0  ±  .1 

-0.001  ±.001 


20.7  ±  1.5 

13.1  ±  1.0 

0.5  ±  .5 

0.4  ±  .4 

0.4  ±  .4 

0.0  ±  .2 

0.0  ±  .2 

-0.001  ±.001 


16.2  ±  2 


35.1  ±  2 


The  first  two  terms  (F')  constitute  the  great  bulk  of  the 
total.  The  remaining  six  terms  (r)  make  up  less  than  a  billion 
more  for  either  year.  The  total  reaches  about  16  billions  as 
the  estimated  circulation  of  money  in  the  United  States  in 
1896.  This  estimate  is  subject  to  error,  but  not  as  much  as 
the  total  of  the  possible  errors  of  individual  terms,  which  is 
over  3  billions.  Even  if  each  of  the  possible  errors  indicated 
were  as  likely  as  not  to  occur,  the  chance  that  in  all  eight 
cases  they  should  all  simultaneously  occur  in  the  same  direc- 
tion is  (i) ^,  or  one  chance  in  256.  We  may,  therefore,  "trust 
to  luck"  that  the  errors  will,  to  some  extent,  offset  each  other. 
In  fact,  the  chance  of  the  error  reaching  the  sum  of  those  of 
the  first  three  terms,  or  3  billions,  is  less  than  a  half.  The 
"probable  error"  can  therefore  be  placed  with  some  confi- 
dence as  less  than  2  billions. 

Dividing  the  figures  we  have  obtained  for  the  total  circula- 
tion of  money  by  the  figures  for  the  amount  of  money  in  cir- 
culation, we  obtain  figures  for  the  velocity  of  circulation. 
These  are  18.6  in  1896  and  21.5  in  1909,  which  show  remark- 
ably little  change. 

Reverting  now  to  the  remark  with  which  we  began  the  dis- 


Sec.  7]  APPENDIX  TO    CHAPTER   XII  473 

cussion  of  money  velocity,  namely,  that  it  circulates  but  sel- 
dom outside  of  banks,  let  us  picture  our  statistical  results  in 
the  light  of  this  fact. 

Evidently,  if  all  money  circulated  once  only,  then  the  bank 
record  for  1896,  showing  about  9^  billions  annually  flowing 
into  and  out  of  the  banks,  would  also  exactly  indicate  the 
volume  of  the  intervening  work  done.  This  would  then  be 
9;^-  bilhons.  But  the  true  figure  is,  as  we  have  shown,  prob- 
ably about  16  billions,  and  consequently  we  infer  that  some 
of  the  9t^-  billions  emanating  from  banks  changes  hands  more 
than  once  before  it  returns. 

Next  let  us  suppose  that  all  of  the  91  bilhons  circulate  once, 
except  the  part  passing  through  the  hands  of  "Nondeposi- 
tors"  (6  bilhons),  and  that  the  latter  circulates  twice.  Then 
3|  billions  circulate  once  only.  Under  this  assumption  we 
can  account  for  3^  +  2X6=  15]  billions  of  exchange  work. 
But  we  have  found  in  fact  16  bilhons.  The  difference  of  about 
half  a  billion  is  chiefly  due  to  the  existence  of  some  money 
which  circulates  more  than  twice  outside  of  banks. 

The  entire  16  bilhons  may  be  roughly  accounted  for  by 
dividing  the  9|  billions  flowing  from  banks  into  three  streams ; 
Sj  bilhons  circulating  once  and  once  only ;  5^  billions,  twice 
and  twice  only ;  and  ^  billion,  three  times.  This  makes  85- 
+  2X5I+  3X1=  16  billions.  Of  the  three  parts,  the 
first  (31  billions)  is  mainly  the  spending  money  drawn  by 
"Other  depositors,"  the  second  (5^  billions)  is  money  with- 
drawn from  bank  for  wages  and  other  payments  to  "Non- 
depositors,"  and  the  third  (|  billion)  is  the  small  amount  not 
otherwise  accounted  for.  This  is  only  a  rough  scheme  of  divi- 
sion.   A  very  small  part  circulates  oftener  than  three  times.^ 

1  It  may  avoid  some  confusion  to  remind  the  reader  that  we  are 
dealing  with  sums  of  money  expended  for  goods,  not  with  individual 
coins.  Many  coins  remain  "in  circulation"  a  long  time  without 
returning  to  bank,  because  used  "in  change."  But  money  used  in 
change  enters  as  a  subtractive  term  in  monetary  expenditures. 
When  $10  are  given  for  an  S8  purchase,  and  $2  are  received  back 
in  change,  $12  have  changed  hands,  but  only  $8  of  monetary  cir- 
culation against  goods  have  been  effected. 


474       THE   PURCHASING   POWER  OF  MONEY     [Append.  XIJ 

Similarly,  for  1909,  of  the  21  billions  flowing  into  and  out 
of  the  banks,  the  13  billions  passing  through  the  hands  of 
"  Nondepositors "  must  have  circulated  twice  or  more  and 
thus  have  accounted  for  26  billions  or  more  of  the  total  circu- 
lation (35  billions),  leaving  21  —  13,  or  8,  to  have  circulated  only 
once.  This  would  account  for  26  +  8  or  34  billions.  The 
entire  35  billions  may  be  accounted  for  by  supposing  the  21 
billions  flowing  from  banks  to  be  divided  into  the  following 
three  streams :  — 

8  billions  circulating  once,  making  8  billions, 
12  billions  circulating  twice,  making  24  bilUons, 
1  billion  circulating  three  times,  making  3  billions. 

The  whole  21  billions,  bank  outflow,  perform  35  billions  of 
circulation  before  returning  to  bank. 

The  first  two  terms  of  the  formula  for  the  monetary  circu- 
lation evidently  give  15 1  billions  out  of  our  estimated  total 
of  16  billions  for  1896,  and  34  out  of  35  for  1909 ;  showing 
that  the  remainder,  unless  it  has  been  greatly  underestimated, 
is  relatively  small.  The  significance  of  this  fact  is  that  the 
terms  most  difficult  to  estimate  statistically  are  least  impor- 
tant. Of  the  two  terms  constituting  the  "first  approxima- 
tion," the  first  and  most  important  is  susceptible  of  the  most 
accurate  determination  of  all,  while  the  second  is  made  up 
chiefly  of  wages,  which  also  are  susceptible  of  statistical 
determination,  or  seem  destined  to  become  so. 

In  fact,  if  we  should,  as  a  statistical  makeshift  for  the  first 
approximation,  merely  add  the  amount  of  money  annually  with- 
drawn from  bank  to  the  annual  money  wages,  we  should,  as  to 
the  year  1896,  account  for  9y  +  ^2  or  14  out  of  16  billions,  leav- 
ing only  2  billions  to  be  otherwise  accounted  for.  In  other 
words,  this  makeshift  —  the  part  most  adapted  to  statistical 
measurement  —  accounts  for  about  88  per  cent  of  the  total 
circulation,  leaving  only  12  per  cent  for  the  part  which  can 
only  be  determined  within  wide  limits.  For  1909,  deposits 
plus  wages  make  up  about  32  billions  out  of  35,  or  over  90 


Sec.  7]  APPENDIX   TO   CHAPTER  XII  475 

per  cent.  A  still  simpler  makeshift  is  to  add  the  deposits 
to  the  total  wages  without  attempting  to  ascertain  the  part 
which  is  paid  in  money.  This  makeshift  might  be  justified 
on  the  ground  that  total  wages  are  more  exactly  ascertain- 
able than  the  part  paid  in  money,  and  that  presumably  the 
money  part  will  maintain  a  fairly  constant  ratio  to  the 
total  wages  from  year  to  year.  The  two  parts  here  indi- 
cated may  be  distinguished  as  the  measurable  part  (com- 
prising the  first  term  of  our  formula  (1)'  and  most  of  the 
second  term),  and  the  conjectural  part,  comprising  the  re- 
mainder of  the  second  term  and  the  other  six  terms.  Even 
if  the  allowance  for  the  conjectural  part  should  prove  to 
be  but  half  the  truth,  the  measurable  part  would  still  con- 
stitute the  great  bulk  of  the  total.  The  measurable  part 
would  therefore  still  be  a  safe  practical  index,  or  barometer 
of  changes  in  the  volume  of  circulation.  Any  excess  of  varia- 
tion in  the  conjectural  part,  as  compared  with  the  measurable 
part,  would,  when  spread  over  the  whole,  produce  a  disturb- 
ance only  one  fourth  as  great.  It  is  reasonable  to  suppose 
that  the  conjectural  and  measurable  parts  will  ordinarily  vary 
together.  If  the  measurable  part  varies  10  per  cent,  it  is  natu- 
ral to  suppose  that  the  conjectural  part,  and  therefore  also  the 
total  of  both,  will  vary  likewise.  But  suppose  this  assump- 
tion erroneous  and  that,  while  the  measurable  part  varies  10 
per  cent,  the  conjectural  part  really  varies  14  per  cent  or  6  per 
cent.  The  difference  between  these  and  10  per  cent,  i.e.  4 
per  cent,  representing  a  supposed  excess  or  deficiency  of  vari- 
ation of  the  conjectural  part,  would  produce  a  difference  of 
only  1  per  cent  in  the  total !  That  is,  the  total,  instead  of 
varying  10  per  cent,  would  vary  11  per  cent  or  9  per  cent. 
Evidently,  therefore,  any  unknown  variation  in  the  conjec- 
tural part  can  cause  only  a  trifling  variation  in  the  result. 
In  other  words,  the  measurable  part  will  always  be  a  good 
index  of  the  total  —  a  reliable  barometer  of  circulation.  If 
we  divide  this  by  the  quantity  of  money  in  circulation,  we 
obtain  a  figure  indicating  the  relative  velocity  of  circulation 
of  money  from  year  to  year.    We  conclude,  therefore,  that 


476       THE    PURCHASING    POWER   OF  MONEY     [Append.  XII 

money  deposits  plus  wages,  divided  by  money  in  circulation, 
will  always  afford  a  good  barometer  of  the  velocity  of 
circulation. 

It  is  not  always  the  absolute  value  of  any  magnitude  we 
find  most  useful,  but  its  relative  value  under  different  con- 
ditions. We  may  compare  the  relative  length  of  two  ships  by 
measuring  their  water  lines,  although  this  method  omits  the 
overhang  at  either  end.  Such  a  comparison  will  apply  roughly 
to  any  two  vessels,  and  with  great  exactness  to  two  ships  of 
the  same  build.  Similarly,  our  proposed  barometer  will  af- 
ford rough  comparisons  for  any  two  coimtries  using  banking 
facilities  in  comparable  degrees,  and  will  afford  fairly  exact 
comparisons  for  two  successive  years  in  the  same  country. 

The  proper  statistical  procedure  would,  therefore,  seem  to  be 
to  provide  for  the  conjectural  part  by  an  estimated  percent- 
age correction,  to  be  applied  to  the  measurable  part  as  a  con- 
stant factor.  Different  correction  factors  will  presumably 
apply  in  different  countries,  as,  let  us  say,  10  per  cent  in  the 
United  States,  20  per  cent  in  England,  30  per  cent  in  France, 
etc.  The  chief  value  of  such  conjectural  corrections  would  be 
to  enable  us  to  compare  roughly  the  circulations  and  velocities 
of  different  countries.  For  comparisons  in  the  same  country 
at  different  times  it  would  be  almost  immaterial  what  per- 
centage correction  were  adopted  or  whether  none  at  all  were 
employed. 

By  means  of  the  method  which  has  been  explained,  it  is  be- 
lieved that  some  interesting  and  valuable  results  can  in  the 
future  be  obtained,  if  statisticians  in  various  lands  will  obtain 
(1)  the  total  money  deposited  each  year  in  banks  (except  by 
other  banks),  or,  what  is  normally  the  same  thing,  the  total 
money  withdrawn  from  banks  (except  by  other  banks) ;  (2) 
the  total  wages  expended,  or,  what  is  practically  the  same 
thing,  the  total  wages  received;  (3)  if  desired,  a  conjectural 
percentage  addition  to  allow  for  the  remaining  and  less  known 
part  of  our  formula ;  (4)  the  total  money  in  circulation.  The 
sum  each  year  of  (1)  and  (2)  corrected  by  (3)  and  divided  by 
(4)  will  be  a  very  accurate  barometer  of  the  velocity  rela- 


Sec.  8]  APPENDIX   TO    CHAPTER   XII  477 

tively  considered,  as  well  as  a  fair  approximation  to  its  abso- 
lute value.  The  omission  of  (3)  will  not  invalidate  the  re- 
sults for  purposes  of  relative  comparison. 

The  importance  of  such  accurate  determinations  can 
scarcely  be  overestimated,  as  the  remarks  on  the  subject  by 
Jevons,  Landry,  and  others  have  shown.  When  we  know  sta- 
tistically the  velocity  of  circulation  of  money,  we  are  in  a 
position  to  study  inductively  the  "quantity  theory"  of  money, 
and  to  discover  the  significance  of  that  velocity  in  reference 
to  crises,  accumulation  of  wealth,  density  of  population, 
rapid  transit,  and  communication,  as  well  as  many  other  con- 
ditions. In  fact  a  new  realm  in  monetary  statistics  is  laid 
open. 

§  8  (to  Chapter  XII,  §  4) 

Interpolating  Values  of  V  for  1897-1908 

To  interpolate  values  for  V  we  split  the  difference  between 
two  extreme  hypotheses :  the  one  of  extreme  steadiness ;  the 
other  of  extreme  variability. 

The  first  of  these  hypotheses  is  that  V  changes  in  a  steady 
progression  from  its  value  of  18.6  in  1896  to  its  value  of  21.5 
in  1909.  This  would  imply  a  perfectly  steady  growth  with 
time,  with  no  temporary  fluctuations.  But  it  seems  unlikely 
that  the  velocity  of  circulation  of  money  should  not  fluctuate 
somewhat  from  year  to  year.  We  have  seen  that,  theoreti- 
cally, there  is  a  tendency  under  normal  conditions  for  money 
expenditures  (MV)  to  keep  pace  with  check  expenditures 
(M'V).  If  this  correspondence  were  perfect,  we  should  have 
the  ratio  of  ilf  F  to  M'V,  if  not  constant,  at  least  changing  in 
a  perfectly  even  manner  with  time.  Now  this  ratio  for 
1896  is  16.7  per  cent  and  in  1909,  9.6  per  cent.  If  we  were  to 
assume  a  perfectly  steady  change  in  this  ratio  during  the  in- 
tervening 13  years,  the  resulting  value  for  V  would  have  to 
vary  considerably.  This  assumption  is  our  second  hypothesis 
of  extreme  variability.  The  following  table  shows  the  re- 
sults of  the  two  extreme  hypotheses.  It  will  be  seen  that 
in  general  there  is  no  great  difference  between  them. 


478       THE   PURCHASING  POWER  OF  MONEY     [Append.  XII 


(1). 

(2) 

Htpothbsis  of 
ExTBEME  Varia- 

(3) 

Tbar 

Htpothesib  op 
Extreme  Steadi- 
ness 

bility 
V 

VARYDJa   AS 
NEEDED  TO    PRE- 
SERVE   EVENLY 

CHANGING  Ratio 
or  MV  TO  AI'V 

Mean  op  two 
I'rbcedino 

1896 

18.6 

18.6 

18.6 

1897 

18.8 

19.4 

19.1 

1898 

19.0 

20.6 

19.8 

1899 

19.3 

24.4 

21.9 

1900 

19.5 

20.4 

20.0 

1901 

19.7 

23.9 

21.8 

1902 

19.9 

23.6 

21.8 

1903 

20.2 

20.9 

20.6 

1904 

20.4 

20.9 

20.7 

1905 

20.6 

23.0 

21.8 

1906 

20.8 

22.5 

21.7 

1907 

21.1 

21.0 

21.1 

1908 

21.3 

18.6 

20.0 

1909 

21.5 

21.4 

21.5 

A  supplementary  calculation  reveals  the  interesting  fact 
that  the  "  hypothesis  of  extreme  variability"  would  make 
money  velocity  fluctuate  approximately  with  deposit  velocity. 
Splitting  the  difference  between  the  two  extreme  hypotheses, 
— that  of  extreme  steadiness  and  that  of  extreme  variability, 
— we  have  what  would  seem  to  be  an  approximately  correct 
estimate  of  actual  velocity.  It  is  probably  correct  in  most 
cases  for  the  first  two  digits.  We  cannot  assume  even  for 
1896  and  1909  that  the  third  digit,  that  beyond  the  decimal, 
is  correct,  much  less  can  we  assume  this  to  be  true  for  the  inter- 
vening years.  But  it  is  sometimes  advisable  to  carry  out  the 
calculations  to  one  digit  beyond  "  the  last  significant  figure." 


§  9  (to  Chapter  XII,  §  5) 

Method  of  Calculating  T 

The  table  in  the  text  is  taken  from  the  final  column  of  the 
following  more  complete  table :  — 


Sec.  9J 


APPENDIX   TO    CHAPTER   XII 


479 


H 

O 

-< 

a 

b 
O 

H 
P 

O 
> 

o 


n 
a 


1 

o 

(11) 

Absolute 
Trade  (T) 

05aiOcciO'-HtjHioTt<ooo(N.-iOi 
oco<ot>i>'-ioco(Mt^a>.-iooo5 

(M(N(N(M(NCOCOCOCOC«3CO'*cCCO 

(10) 
Relative 

Trade 

Weighted 

average 

2x(5)+lx(9) 

TO 

.-Hf0f-l«0t>^00OOI>T}<OG0>O 
OOOiOOOCNi-iCOWTtiiOOTj^iO 

(9) 

(8)  Re- 
duced to 
Calendar 
Years 

CO  00  O  CO  O  lO  lO  O  CO  .-H  lO  Tj<  rt<    1 
t^  t^  00  Oi  05  O  "-I  (N  (N  ■*  lO  lO  »0    1 

1 

g 

-So 

g 
Q 

(8) 

Weighted 

average 

of  two 

preceding 

2x(6)+lx(7) 

CO 

(M-^COOt^OOOOCOOOOSO 
t^t>000001O'-iMMC0iOC0Tti«0 

I— li-tl-Hi-4i— ll— Ii-ItHi-H 

(7) 

P.  0. 

Letters 
Carried 

1  CO00(N00iO(M^»O^00t^(M(N 

1— 1  1— 1  1— 1  1— 1  1— (  i-H  I— 1 

(6) 

R.  R. 

tons 
Carried 

t^OSrHOOt^OOOiOt^-^—KNlN 
«>  t^  05  05  O  O  I-H  CO  (M  TjH  <£>  t>  lO    1 

% 

m 

>< 

% 
a 
z 

■< 

o 

o 

o 
g 

s 

B 

(5) 

Weighted  Average 

of  Three  Preceding 

20x(2)+3x(3)  +  lx(4) 

^ 
M 

<lOOOS(M'-H050iOi005CC(N»OC^ 
0000'-i,-t(N(NCONTl<iOO'<l<iO 

(4) 

Sales  of 
Stocks 

»0t^C0<O00O05»-it^C0'*cCit^lO 

iot>'-Ht^cocooo;ooocoooo505'-i 

1— ll— It— l(Ni— It— li— (C^C^i— li— IC^ 

(3) 

Exports 

and 
Imports 

cot^coO'-ir^(N'-<'-ia)'^t^oio 

t>-00050000000'-i'-i'-i(N 

(2) 

Internal 
Commerce 

a>coi-ii-irHioai05ioCT>(Nt^ooeo 

OOO— It-It-KMt-iCOIN-^iOCOtJhiO 

(I) 
Year 

?Or>OOOiO^(NCOTj<U5COt^OOOi 
OOiOJOiOOOOOOOOOO 
00000000O5O5O5O5O>O5O>O5aiO5 
I— li-Hl-H»Hl— l»-tl-li— (i-Hi— (tHi— IrHrH 

480       THE   PURCHASING   POWER   OF  MONEY     [Append.  XII 

This  table  is  constructed  as  follows :  — 

Column  (2)  is  constructed  for  1900-1909  from  monthly 
figures  on  Internal  Commerce  pubUshed  in  the  Monthly 
Su7nmary  of  Commerce  and  Finance  of  the  United  States. 
By  taking  the  monthly  figures  it  was  possible  to  obtain  re- 
sults for  calendar  years.  This  column  is  an  average  of  sepa- 
rate indices  for  the  following  articles  for  which  records  were 
available.  The  original  figures  give  the  quantities  of  each 
article  brought  into  the  principal  cities  of  the  United  States. 
These  quantities  were  each  multiplied  by  an  assumed  price 
which  remained  as  a  constant  multipUer  for  every  year.  The 
products  were  then  added  together  and  the  figures  thus  ob- 
tained taken  to  represent  the  total  trade  in  these  commodi- 
ties, and  to  be  a  barometer  of  the  relative  internal  commerce 
in  the  United  States. 

The  articles  referred  to,  and  the  dates  for  which  data 
were  used  (as  well  as  the  price  factors  employed  as  explained 
below)  are  as  follows :  — 


Articles 

Price 

Dates 

Cotton 

$45.00  bale 

Jan., 

1900-1909 

Rice 

5.00  sack 

Aug. 

, 1900-1909 

Fruit 

1000.00  car 

Feb., 

1900-1909 

Lumber  (Shipments 

from    South  and 

Southwest) 

.02  ft. 

Feb., 

1900-1909 

Boots  and  Shoes    . 

80.00  case 

Mar. 

,  1900-1909 

Anthracite  Coal     . 

4.74  ton 

Jan., 

1900-1909 

Bituminous  Coal    . 

2.74  ton 

Jan., 

1900-1909 

Pig  iron,  coke,  and 

anthracite      .     . 

19.40  gross  ton 

July, 

1902-1909 

Petroleum      (Ship- 

ments by  water 

from  Texas)  .     . 

1.80  bbl. 

Nov. 

,  1901-1909 

Cattle  (Receipts  at 

five  cities)       .     . 

55.00  head 

Jan., 

1900-Dec.,  1903 

Cattle  (Receipts  at 

seven  cities)  .     . 

55.00  head 

Jan., 

1900-1909 

Hogs   (Receipts  at 

five  cities)       .     . 

18.00  head 

Jan., 

1900-Dec.,  1903 

Sec.  9] 


APPENDIX   TO   CHAPTER   XII 


481 


Articles 


Pbiob 


Dates 


Hogs   (Receipts  at 

seven  cities)  . 
Sheep  (Receipts  at 

five  cities) 
Sheep  (Receipts  at 

seven  cities)   .     . 
Wheat  (Receipts  at 

eleven  cities) 
Wheat  (Receipts  at 

twelve  cities) 
Wheat  (Receipts  at 

fourteen  cities)    . 
Wheat  (Receipts  at 

fourteen  cities)    . 
Wheat  (Receipts  at 

fifteen  cities) 
Corn    (Receipts  at 

twelve  cities) 
Corn    (Receipts   at 

fourteen  cities)   . 
Corn    (Receipts   at 

thirteen  cities)    . 
Corn    (Receipts   at 

fifteen  cities) 
Oats    (Receipts    at 

twelve  cities) 
Oats    (Receipts   at 

fourteen  cities)   . 
Oats    (Receipts   at 

fifteen  cities) 
Barley  (Receipts  at 

nine  cities)     .     . 
Barley  (Receipts  at 

ten  cities)       .     . 
Barley  (Receipts  at 

eleven  cities) 
Barley  (Receipts  at 

twelve  cities) 
Barley  (Receipts  at 

thirteen  cities)    . 
Barley  (Receipts  at 

fourteen  cities)    , 
Rye    (Receipts    at 

eleven  cities) 
Rye    (Receipts    at 

twelve  cities) 
Rye    (Receipts    at 

thirteen  cities)    . 
Rye    (Receipts    at 

fourteen  cities)   . 


$18.00  head 

4.00  head 

4.00  head 

1.00  bu. 

1.00  bu. 

1.00  bu. 

1.00  bu. 

1.00  bu. 

.75  bu. 

.75  bu. 

.75  bu. 

.75  bu. 

.53  bu. 

.53  bu. 

.53  bu. 

.70  bu. 

.70  bu. 

.70  bu. 

.70  bu. 

.70  bu. 

.70  bu. 

.80  bu. 

.80  bu. 

.80  bu. 

.80  bu. 


Jan.,  1900-1909 
Jan.,  1900-Dee.,  1903 
Jan.,  1900-1909 
June,  1903 

Apr.,  1903-Dec.,  1903 
May,  1904-1909 
May,  1904-1909 
Apr.,  1903-1909 
Apr.,  1903-Dec.,  1903 
Jan.,  1904-1909 
Feb.,  1906-Feb.,  1907 
Apr.,  1903-1909 
Apr.,  1903-Dec.,  1903 
Feb.,  1906-Feb.,  1907 
Apr.,  1903-1909 
June,  1903-Aug.,  1908 
Apr.,  1903-May,  1908 
Sept.,  1903- June,  1908 
Feb.,  1906-Sept.,  1908 
Feb.,  1904-1909 
Apr.,  1903-1909 
Apr.,  1903-June,  1906 
Jan.,  1905^Aug.,  1908 
Apr.,  1904-1909 
Apr.,  1903-1909 


2i 


482       THE    PURCHASING   POWER  OF  MONEY     [Append.  XII 


Articles 

PaicB 

Dateb 

Flaxseed   (Receipts 

at  four  cities) 

$1.50  bu. 

Feb. 

,  1905-1909 

Flaxseed  (Receipts 

at  five  cities) 

1.50  bu. 

Jan., 

1904-1909 

Flaxseed   (Receipts 

at  six  cities)  .     . 

1.50  bu. 

Jan., 

1904-1909 

Flour  (Receipts  at 

ten  cities)  ,     .     . 

4.80  bbl. 

Apr. 

1903-1909 

Flour  (Receipts  at 

eleven  cities) 

4.80  bbl. 

Jan., 

1904-1909 

Flour  (Receipts  at 

twelve  cities) 

4.80  bbl. 

Mar. 

,  1904-1909 

Flour   (Receipts  at 

thirteen  cities)    . 

4.80  bbl. 

Apr., 

1903-1909 

Petroleum      (Ship- 

ments   by  Pipe- 

lines—  Reg.   De- 

liveries.       App. 

Field     .... 

1.80  bbl. 

Jan., 

1901-1909 

These  articles  are  representative  for  the  trade  of  the 
country  and  may  well  serve  as  a  barometer  of  that  trade. 
Yet  the  amount  of  trade,  actually  consisting  of  the  sales  of 
these  articles  in  the  few  cities  concerned,  constitutes  of 
course  only  a  very  small  part  (probably  less  than  one  tenth 
of  1  per  cent)  of  the  total  trade  of  the  country. 

The  actual  figures  first  obtained  were  all  divided  by  two 
before  being  entered  in  column  (2)  in  order  to  bring  them 
down  to  a  scale  more  comparable  with  the  figures  of  column 
(3).  Since  not  all  of  the  commodities  were  quoted  in  all 
the  years,  the  table  had  to  be  "pieced  out"  for  the  defective 
years  by  the  principles  of  proportion  as  already  exemplified. 
As  the  statistics  of  the  Monthly  Summary  go  back  only  to 
1900,  the  table  had  to  be  "pieced"  back  to  1896.  This  was 
done  by  using  data  from  the  statistical  abstract  of  the  United 
States  and  the  abstract  of  the  United  States  Census  for  1900. 
The  only  figures  obtainable  for  important  articles  in  internal 
trade  were  those  for  grain,  received  during  calendar  years  at 
fifteen  principal  primary  markets,  and  for  the  estimated 
national  consumption  during  fiscal  years  of  the  following 


Sec.  9]  APPENDIX  TO   CHAPTER   XII  483 

articles,  chiefly,  or  largely,  of  domestic  production:  cotton, 
wool,  bituminous  coal,  pig  iron,  iron  and  steel  railroad  bars, 
and  "distilled  spirits,  wines,  and  malt  liquors." 

The  fiscal  year  figures  were  taken  from  1896  to  1901  inclu- 
sive and  reduced  to  calendar  years  on  the  assumption,  for 
instance,  that  the  true  figure  for  the  calendar  year  1896  is  the 
average  of  those  for  the  two  fiscal  years  ending  June  30, 1896, 
and  June  30,  1897.  In  this  way  we  get  hypothetical  calen- 
dar year  figures  for  1896  to  1900.  These  figures  and  those  for 
grains,  which  were  already  for  calendar  years,  were  then 
reduced  by  a  factor  so  that  each  was  made  to  be  111  for  1900, 
the  number  for  that  year  found  by  the  calculations  involv- 
ing the  articles  in  the  series,  1900-1909.  The  figures  thus 
found  were  then  averaged  with  weights  selected  to  correspond 
with  the  estimates  of  their  respective  importance  as  judged 
from  the  estimates  of  their  national  consumption  values  and 
from  the  fact  that  some  of  them  are  indicators  of  large  re- 
lated businesses.  The  weights  chosen  were  :  for  grains 
(including  wheat,  wheat  flour,  corn,  rye,  oats,  barley,  malt, 
and  pease  0  >  20  ;  for  bituminous  coal,  iron  and  steel,  liquors, 
and  cotton,  5  each  ;  and  for  pig  iron  and  wool,  1  each. 

The  data  for  1896-1899  are  far  inferior  to  those  for  1900- 
1909  taken  from  the  Monthly  Summary,  and  this  for  three 
reasons  :  (1)  because  they  are  so  few  in  number  ;  (2)  be- 
cause all  except  the  grains  are  for  fiscal  years  and  the  hypo- 
thetical correction  to  calendar  years  is  subject  to  error; 
and  (3)  because  all  except  the  grains  are  very  rough  estimates 
of  consumption,  not  based  on  shipments  or  receipts,  but  based 
on  estimated  production,  corrected  for  exports  and  imports, 
which  three  elements  are  all  subject  to  error. 

We  should  not  be  surprised,  therefore,  to  find  larger  errors 
in  the  resulting  figures  for  1896-1899  than  for  1900-1909. 
In  fact,  we  shall  see  that  such  is  probably  the  case. 

For  carrying  out  the  laborious  operations  involved  in 
ascertaining  the  index  numbers  from  1900  to  1908,  I  am  in- 

*  See  Statistical  Abstract  of  United  States,  1908,  p.  523. 


484       THE    PURCHASING   POWER   OF  MONEY     [Append.  XII 


debted  to  one  of  my  undergraduate  students,  Mr.  Robert  N. 
Griswold,  and  for  bringing  them  down  to  1909,  to  one  of  my 
graduate  students,  Mr,  W.  Y.  Smiley. 

Column  (3)  is  also  based  on  laborious  calculations  which 
were  performed  by  Mr.  Griswold.  The  materials  were  also 
taken  from  the  Monthly  Summary  of  Finance  and  Commerce 
and  covered  23  staple  articles  of  import  and  25  for  export. 
The  quantities  of  each  were  multiplied  by  a  uniform  price,  and 
the  sum  of  the  resulting  figures  for  imports  and  exports  was 
taken.  The  articles  of  imports  (with  the  price  multipliers 
used)  were :  — 

Imports  of  the  United  States  1896-1909 
(Bulletin  of  Bureau  of  Commerce  and  Statistics) 


Cocoa     . 

.13  lb. 

Raw  silk    .     .     .         .04  lb. 

Tea    .     . 

.16  lb. 

Hides   and  skins 

Coffee     . 

.07  lb. 

(other  than  fur 

Sugar 

.02  lb. 

skins) 11  lb. 

Lemons 

.04  lb. 

Raw  wool       .     .     .     .13  lb. 

Bananas 

1.60  bunch 

India  rubber  ...     .78  lb. 

Cheese    . 

.17  lb. 

Boards   and   sawed 

Distilled     spirits 

lumber   .     .     .     18.00  M.  ft. 

(imported)    . 

5.00  gal. 

Coal    (anthracite  & 

Sparkling  wines 

bituminous)     .       2.60  per  t. 

(Champagne) 

29.00  doz.  qts. 

Tin 28  1b. 

Leaf  tobacco    . 

1.00  lb. 

Copper  (pigs,  bar, 

Cotton    . 

ingots,  old,  un- 

(mfg. cloth) 

.09  sq.  yd. 

manufactured)          .17  lb. 

Linens  (mfg.  flax 

Pig  iron     .     .     .     23.00  per  t. 

hemp,  or  ramie ] 

.50  sq.  yd. 

Sodium  nitrate        38.00  per  t. 

Woolen  dress 

goods 

• 

.21  sq.  yd. 

The  articles  of  exports  were :  — 

Exports  of  the  United  States  1896-1909 
(Bulletin  of  Bureau  of  Commerce  and  Statistics) 

Wheat  ....       1.00  bu. 
Flour     ....       4.80  bu. 
Tobacco  leaf       .         .10  lb. 
Sawed  lumber     .     23.00  M.  ft. 
Wood  pulp     .     .  .015  lb. 

Linseed  oil  (cake)        .014  lb. 
Refined  illuminating 

oil 07  gal. 

Cottonseed   oil   .         .40  gal. 
Coal       ....       3.70  ton 

Copper 17  1b. 

Steel  rails        .     .     31.60  ton 
Sheet  steel      .     .         .0135  ton 


Cattle     .     .     . 

55.00  head 

Hams      .     .     . 

.11  lb. 

Salt  pork     .     . 

.09  lb. 

Fresh  beef 

.10  lb. 

Canned  beef     . 

.11  lb. 

Bacon 

.11  lb. 

Lard        .     .     . 

.11  lb. 

Butter    .     .     . 

.21  lb. 

Sole  leather 

.21  lb. 

Boots  and  shoes 

2.75  pr. 

Raw  cotton 

.48  bale 

Cotton  cloth    . 

.09  yd. 

Corn       .     .     . 

.60  bu. 

Sec.  9]  APPENDIX   TO   CHAPTER   XII  485 

The  statistics  of  exports  and  imports  are  probably  fifty 
times  as  full  as  those  of  internal  commerce  and  therefore 
(on  the  principle  that  probable  errors  vary  inversely  as  the 
square  root  of  the  fullness  of  returns)  some  seven  times  as  accu- 
rate. But,  on  the  other  hand,  exports  and  imports  represent 
less  than  1  per  cent  as  much  trade  as  the  internal  commerce 
of  the  United  States,  and,  by  the  principles  already  explained 
in  previous  chapters,  should  count  in  the  equation  of  exchange 
only  at  half  its  value,  one  of  the  parties  in  the  exchange  being 
a  foreigner.  In  spite,  however,  of  the  diminutive  character 
of  external  commerce,  it  is  to  some  extent  an  index  of  internal 
commerce;  since  a  vast  amount  of  internal  business  is  a  pre- 
liminary to  exports  and  a  sequel  to  imports,  while  perhaps  a 
still  larger  amount  is  in  other  ways  indirectly  related  to  such 
commerce.  By  balancing  these  and  other  considerations,  the 
relative  weights  to  be  assigned  to  the  external  and  internal 
trade  were  selected  as  given  in  column  (5). 

Column  (4)  gives  the  sales  of  stocks  according  to  the 
ordinary  figures  as  given,  for  instance,  in  the  Financial  Review. 
These  figures  are,  of  course,  not  for  values,  but  for  amounts. 

Column  (6)  gives  the  figures  for  tons  of  freight  carried  by 
railroads  according  to  Poor's  Railroad  Manual  for  fiscal  years. 

Column  (7)  gives  the  figures  for  pieces  of  first-class  mail 
matter  carried  in  fiscal  years.  These  figures  were  kindly 
supplied  by  the  Post  Office  Department.  They  are  lacking 
for  1896. 

We  have  still  to  describe  the  method  employed  for  combin- 
ing columns  (2),  (3),  (4),  (6),  (7). 

The  first  three  are  regarded  as  constituting  a  group  by 
themselves,  representing  direct  indices  of  trade :  and  the  last 
two  are  regarded  as  constituting  another  group  of  indirect 
indices. 

The  direct  indices  are  combined  by  weighting  the  internal 
commerce,  twenty,  the  exports  and  imports,  three,  and  sales 
of  stocks,  one.  These  weights  are,  of  course,  merely  matters 
of  opinion,  but,  as  is  well  known,  wide  differences  in  systems  of 
weighting  make  only  slight  differences  in  the  final  averages. 


486       THE   PURCHASING   POWER  OF  MONEY     [Append.  XII 

In  this  way,  column  (5)  is  found. 

As  to  the  relative  weights  to  be  given  to  the  railroad  and 
post  office  statistics,  the  former  were  weighted  as  two  and  the 
latter  as  one.  Railway  tonnage  represents  almost  every  con- 
ceivable commodity  in  commerce  and  comes  far  closer  to 
actual  trade  than  post  office  letters. 

After  railroad  and  post  ofl&ce  indexes  are  thus  combined, 
the  transition  from  fiscal  to  calendar  years  is  made  on  the 
assumption  that  the  figures  for  a  calendar  year  are  the  mean 
of  the  figures  for  the  fiscal  years  ending  June  30  of  that  year 
and  June  30  of  the  next  year. 

In  this  way  column  (9)  is  obtained. 

From  columns  (5)  and  (9)  column  (10)  is  obtained  by 
weighting  (5)  two,  and  (9)  one. 

Finally,  column  (11)  is  found  by  magnifying  the  figure  of 
column  (10)  in  the  ratio  fff  in  order  to  make  the  figure  for 
the  base  year,  1909,  equal  to  399  billions  of  dollars,  —  the  total 
value  of  the  left  side  of  the  equation  (MV  +  M'V). 

The  probable  errors  in  the  values  of  T  which  have  been 
calculated  are  believed  to  be  some  5  to  10  per  cent  for  the 
years  1900-1909  and  10  to  15  per  cent  for  the  years  1896-1900. 

§  10  (to  Chapter  XII,  §  5) 

Method  of  Calculating  P 

The  table  in  the  text  for  index  numbers  of  prices  is  taken 
from  the  last  column  of  the  table  on  page  487. 

Column  (2)  gives  the  index  numbers  of  the  United  States 
Labor  Bureau  (No.  81,  March,  1909,  p.  204). 

I  am  under  obligations  to  the  Commissioner  of  Labor,  Mr. 
Neill,  for  his  courtesy  in  supplying  me  with  the  figure  for  1909 
in  advance  of  publication. 

Column  (3)  is  taken  from  the  Bulletin  of  the  Bureau  of 
Labor,  July,  1908,  p.  7. 

Column  (4)  is  from  "The  Prices  of  American  Stocks,  1890- 
1909,"  by  Wesley  C.  Mitchell,  Journal  of  Political  Economy^ 


Sec.  10] 


APPENDIX   TO    CHAPTER   XII 


487 


May,  1910.     These  figures  are  doubtless  the  best  yet  avail- 
able in  this  difl&cult  subject. 

Index  Numbers  of  Prices 


(1) 

Year 

(2) 

Wholesale, 

258 
Commodities 

(3) 
Waoes 

(4) 

FORTT 

(5) 
Weighted 
Average 

(6) 
Column  (5) 
reduced  to 

PER  Hour 

Stocks 

30x(2)+lx(3)+3x(4) 

Basis  of  100  in 

34 

1909 

1896.     .     . 

90 

100 

77 

89 

63.3 

1897.     .     . 

90 

100 

84 

90 

63.7 

1898.     .     . 

93 

100 

94 

93 

66.2 

1899.     .    . 

102 

102 

128 

104 

73.8 

1900.    .     . 

111 

105 

134 

113 

80.2 

1901  .     .     . 

109 

108 

211 

118 

83.7 

1902.     .     . 

113 

112 

250 

125 

88.7 

1903  .     .     . 

114 

116 

201 

122 

86.5 

1904.    .    . 

113 

117 

192 

120 

85.1 

1905.    .    . 

116 

119 

250 

128 

90.8 

1906.    .     . 

123 

124 

267 

136 

96.5 

1907.    .    . 

130 

129 

204 

137 

97.2 

1908.    .     . 

123 

— 

201 

130 

92.2 

1909.     .     . 

127 

— 

277 

141 

100.0 

The  general  index  number  in  column  (5)  is  a  weighted  aver- 
age of  the  figures  in  the  three  preceding  columns,  the  weights 
being  essentially  the  same  as  those  used  by  Professor  Kem- 
merer  and  for  the  same  reasons.^  For  ease  in  computation  the 
weights  are  taken  in  integers,  viz.  30  for  column  (2),  1  for 
column  (3)  and  3  for  column  (4).  This  calculation  brings  the 
table  down  through  1907.  As  column  (3)  is  defective  for 
1908-1909,  these  years  and  1907  are  worked  out  as  averages 
of  columns  (2)  and  (4),  the  weights  being  the  same  as  already 
mentioned.  The  result  is  two  series  of  figures,  one  for  all  three 
columns  ending  in  1907,  and  the  other  for  two  columns  begin- 
ning in  1907.  As  in  this  case  it  happens  that  both  series  have 
the  same  figure  (137)  for  1907,  no  corrections  need  be  made  in 
1908  and  1909.  The  probable  errors  in  the  figures  for  P  may 
be  placed  as  about  5  to  10  per  cent. 


1  See  Money  and  Credit  Instruments,  New  York  (Holt),  1909, 
p.  139. 


488       THE   PURCHASING   POWER   OF  MONEY     [Append.  XII 

§11  (to  Chapter  XII,  §7) 
Mutual  Adjustments  of  Calculated  Values  of  M,  M',  V,  V,  P,  T 

There  are  various  methods  of  calculating  the  best  adjust- 
ments, involving  the  theory  of  least  squares.  But  the  prob- 
lem may  be  greatly  simplified  by  dividing  the  process  into  a 
few  separate  steps.  First,  we  ascertain  the  best  adjustments  of 
the  calculated  values  of  each  side  of  the  equation  of  exchange 
considered  as  a  whole.  We  shall  need  to  exercise  judgment  in 
deciding  the  relative  errancy  of  the  two  sides,  but  the  total 
adjustments  are  so  small  that  differences  in  judgment  could 
not  make  much  difference  in  the  results. 

After  a  careful  weighing  of  all  the  evidence,  it  is  believed 
that  the  errors  in  the  right  side  (PT)  are  liable  to  be  about 
double  those  in  the  left  (MV  -\-M'V').  Accordingly,  the 
discrepancy  between  the  two  sides  is  corrected  by  changing 
PT  twice  as  much  as  MV  +  M'V ;  that  is,  by  applying  to 
PT  a  correction  equal  to  two  thirds  of  the  total  discrepancy, 
and  by  applying  the  remaining  one  third  to  MV  -\-  M'V, 
the  two  corrections  being,  of  course,  opposite  and  such  as  to 
bring  the  two  sides  into  agreement.  Thus,  for  1899,  the  total 
discrepancy  is  5  per  cent,  of  which  we  assign  about  a  third, 
say  2  per  cent,  to  MV  -\-  M'V,  and  the  remaining  3  per 
cent  to  PT.  That  is,  we  propose  to  increase  the  calculated 
figures  for  ilf  F  +  M'V  by  2  per  cent  and  decrease  those  of  PT 
by  3  per  cent.  The  result  will  bring  them  nearly  into  agree- 
ment at  185  biUions.  Sometimes  the  results  will  not  exactly 
agree,  as  this  method  of  adding  and  subtracting  percentage 
corrections  is  only  approximately  correct ;  but  any  remaining 
sUght  discrepancies  are  readily  adjusted  by  slight  empirical 
changes  in  the  factors.  The  result  is  shown  in  the  Figure  20, 
which  gives  MV -\- M'V  and  PT  (reduced  by  dividing  by 
1.11)  as  originally  calculated,  and  a  mean  (dotted)  curve 
which  is  the  revised  estimate  of  both  MV  +  M'V  and  PT. 

The  corrections  which  are  thus  made  in  MV  -\-  M'V  and 
PT,  by  which  they  are  brought  into  mutual  agreement,  are 


Sec.  11] 


APPENDIX   TO    CHAPTER   XII 


489 


small;  but  the  corrections  necessary  in  the  individual  factors, 
M,  F,  M',  V,  P,  T,  are  smaller  still.  We  assume,  for  simphc- 
ity,  that  the  percentage  corrections  to  be  made  in  M  and  M' 
are  equal  to  each  other  and  also  that  the  corrections  to  be 
made  in  V  and  V  are  equal  to  each  other.  This  is  a  reason- 
able assumption ;  but  even  if  some  other  assumption  were 
made,  the  final  results  would  be  scarcely  changed. 


::t:::::::::::::: 

fffH 

-X+i: 

1: 



^Ililll'IIHillll 

800  x ± 

coo  -  4= ,  s 

-- 

- 

:: 

-,,'----,,%■■----- 

UT~lf 

^ 



M-'---'-'"W-- 

ay  EK       II  • 

..'- 

[tl::z 

-- 

J 

::.::: X-,;. 

|K  1' 

•     _.  5. 

5: 

^  ■' :  n 

E . '  I  _ 

S(>  i|^y  4iR  Ht  rrf 'rn 

~r  ' 

1 

-  - 

0 ±±:::::: 

--  ---  _-_^| ^. 

-.:..::;  :;::±::;; 

I89G    IS.S7    1893    I8S 

«    ISOO    1901      1902    IS 

03    1304 

I903    1 

90 

6  190 

7   ISO 

8  1909 

Fig.  20. 


A  correction  of  1  per  cent  simultaneously  in  M  and  M' 
will  produce  a  correction  of  1  per  cent  in  AIV  -{-  M'V. 
Likewise  a  correction  of  1  per  cent  simultaneously  in  V  and 
V  will  produce  a  correction  of  1  per  cent  in  MV  -\-  M'V. 
We  may  then  regard  the  correction  of  MV  -\-  M'V  as 
practically  consisting  of  two  parts :  one,  the  correction  of  M 
and  M' ;  and  the  other,  the  correction  of  V  and  V.  As  the 
Af' s  are  more  accurately  ascertained  than  the  F's,  theip  correc- 
tion should  be  smaller.  Thus,  for  1897,  the  total  correction 
assigned  to  MV  -\-M'V'  is  3  per  cent,  of  which  we  assign 
1  per  cent  to  M  and  M',  and  the  remaining  2  per  cent  to  V 


490       THE   PURCHASING   POWER   OF  MONEY     [Append.  XII 

and  v.  That  is,  we  increase  the  calculated  values  of  M  and 
M'  by  1  per  cent  and  those  of  V  and  V  by  2  per  cent, 
thus  effecting  (approximately)  the  desired  increase  of  3  per 
cent  in  MV  -{-M'V.  In  like  manner  the  total  correction 
assigned  to  PT  is  distributed  over  P  and  T,  assigning  the 
major  part  to  T.  By  thus  distributing  the  corrections  over 
(1)  M  and  M\  (2)  V  and  V,  (3)  P,  and  (4)  T,  we  find  that 
only  very  slight  individual  corrections  are  needed,  the  maxi- 
mum being  only  5  per  cent  and  the  vast  majority  (50  out  of 
56  cases)  not  exceeding  2  per  cent.  In  fact,  a  decided  major- 
ity (35  out  of  56  cases)  are  within  1  per  cent.  It  is  really 
astonishing  to  think  that  a  correction  of  only  2  per  cent  or 
less  is  usually  required  in  our  calculated  values  of  M,  M',  F, 
F',  P,  T,  in  order  to  make  them  conform  perfectly  to  the 
equation  of  exchange.  In  fact,  2  per  cent  is  less  than  what 
might  naturally  be  considered  the  probable  error  in  most  of 
the  figures  as  calculated.  This  fact  justifies  confidence  in  the 
general  correctness  of  our  results. 

Having  thus  corrected,  by  mutual  adjustment,  all  the 
factors  in  the  equation  of  exchange,  we  are  left  with  a  figure 
for  P  which  is  not  100  per  cent  for  any  one  year.  As  we 
prefer  to  call  1909  the  unit  year,  the  figures  for  P  are 
adjusted  on  that  basis  and  the  figures  for  T  accordingly. 
This  change  disturbs  the  system  of  corrections  as  measured 
relatively  to  the  original  figures.  It  reduces  to  zero  the  cor- 
rection of  P  for  1909.  In  general,  it  makes  smaller  the  cor- 
rections for  P  and  T  for  years  near  1909  and  makes  corre- 
spondingly larger  those  for  years  remote  from  1909.  But, 
even  so,  the  corrections  never  exceed  10  per  cent  for  T  nor  6 
per  cent  for  P.  As  the  entire  scheme  of  corrections  thus  out- 
lined is  a  matter  of  judgment  and  each  figure  was  frankly  "doc- 
tored "  on  its  own  individual  merits  in  view  of  all  the  circum- 
stances in  the  case,  it  seems  inadvisable  to  burden  these  pages 
by  any  fuller  statement  of  the  voluminous  details  of  the  pro- 
cess. The  results  as  shown  in  Figures  13,  14,  15,  and  16, 
already  given  in  the  text,  speak  for  themselves. 


Sec.  12] 


APPENDIX   TO   CHAPTER   XII 


491 


§  12  (to  Chapter  XII,  §  17) 

Credit  and  Cash  Transactions.    Comparison  with  Kinley's  Esti- 
mates 

These  figures  agree  surprisingly  well  with  what  might  be 
expected  from  a  rougher  calculation  from  Kinley's  investiga- 
tions. For  July  1,  1896,  he  found  that  money  deposits  con- 
stituted 7.4  per  cent  of  all  deposits  and,  on  March  16,  1909,  5.9 
per  cent.  Both  of  these  figures  are  too  low  to  represent  the 
percentage  of  money  transactions,  for  the  reason  that  money 
often  circulates  more  than  once  before  being  deposited, 
whereas  checks  in  general  circulate  but  once.  The  figure  for 
1896,  especially,  is  too  low,  because  of  the  excessive  amounts 
of  checks  deposited  on  July  1.  In  fact,  it  was  largely  be- 
cause the  1896  figures  had  been  criticized  in  this  respect  that 
Kinley  made  the  1909  investigation.  He  did  not,  of  course, 
take  the  figures  of  deposits  as  indicating  exactly  the  ratios  of 
check  and  money  transactions.  He  recognized  the  fact  that 
these  would  give  too  low  a  ratio  for  money  and  too  high  a  ratio 
for  checks.  He  expressed  the  belief  that  a  safe  minimum  for 
check  transactions  in  1896  was  75  per  cent  ^  and  in  1909,  88 
per  cent,  implying  that  25  per  cent  and  12  per  cent  were  safe 
maxima  for  monetary  circulation.  Professor  Kinley's  pur- 
pose seems  to  be  to  establish  safe  maxima  rather  than  to  at- 
tempt exact  estimates.  Tabulating  Kinley's  figures,  we  have 
for  money  transactions  expressed  in  percentage  of  all  trans- 
actions :  — 


(1) 

(2) 

(3) 

(4) 

(5) 

Year 

1896     .... 
1909     .... 

Maximum 
(Kinley's 
estimate) 

25 
12 

Minimum     (as 

indicated  by 

deposits) 

7.4 

5.9 

Mean  of  two 
preceding 

16i 
9 

Present 
estimate 

14 
9 

^  His  original  estimate  for  a  safe  minimimi  was  80  per  cent.  But 
in  the  Journal  of  Political  Economy,  Vol.  V,  p.  172,  and  in  "Money,'' 
p.  44,  and  pp.  108,  14,  he  takes  75  per  cent  as  safer. 


492       THE    PURCHASING   POWER  OP  MONEY     [Append.  XII 

According  to  this  table,  if  we  take  the  percentage  of  money 
in  bank  deposits  as  a  lower  limit  of  the  percentage  of  money 
transactions,  and  if  we  take  Kinley's  estimates  as  a  safe  upper 
limit,  and  if  we  split  the  difference  between  these  two  limits, 
we  shall  reach  almost  ^  the  same  results  as  already  reached  by 
the  more  exact  calculations  in  this  book,  which  results  are 
given,  for  comparison,  in  the  last  column.  Thus  the  results  of 
this  book  strikingly  confirm  those  of  Professor  Kinley.  They 
also  agree  remarkably  well  with  the  prevailing  impression 
among  business  men  that  about  90  per  cent  of  trade  is  now 
performed  by  means  of  checks. 

ADDENDUM   FOR   SECOND   EDITION 

The  figures  in  this  second  edition  have  been  brought  down 
to  date  by  adding  data  for  1910,  1911,  and  1912  to  the  tables 
on  pages  304  and  317  and  inserting  a  new  diagram  between 
pages  306  and  307.  (For  full  explanations  as  to  these  figures 
see  page  xxiii  of  this  book  and  "  '  The  Equation  of  Exchange,' 
1896-1910,"  American  Economic  Review,  June,  1911 ;  "  '  The 
Equation  of  Exchange  '  for  1911  and  Forecast,"  ibid.,  June, 
1912 ;  and  "  '  The  Equation  of  Exchange '  for  1912  and  Fore- 
cast," ibid.,  June,  1913.) 

Professor  Wesley  Clair  Mitchell  has  kindly  shown  me  the 
sheets  of  his  forthcoming  book  (University  of  California 
Press)  on  Business  Cycles,  in  which  he  has  reestimated  the 
deposits  subject  to  check  (M')  by  somewhat  different  methods 
and  with  the  aid  of  some  data  not  available  when  the  present 
book  was  written. 

If  I  were  rewriting  this  book,  I  should  adopt  Professor 
Mitchell's  more  perfect  methods  and  results.  But  to  do  so 
now  would  involve  a  disturbance  of  a  large  number  of  plates 
for  the  sake  of  a  very  small  net  change  in  final  results.     I 

1  If  we  take  Kinley's  original  "  safe  minimum  "  for  cheeks  of  80 
per  cent,  and  consequently  the  "  safe  maximum  "  for  cash  as  20  per 
cent,  we  shall  obtain  in  the  above  table  14  per  cent,  instead  of  the 
figure  I62,  which  would  make  the  last  two  columns  agree  absolutely. 


ADDENDUM   FOR   SECOND    EDITION 


493 


content  myself,  therefore,  by  here  giving  a  table  of  Professor 
Mitchell's  figures,  including  columns  showing  how  much  mine 
are  larger  or  smaller. 

Professor  Mitchell's  Estimates  of  Deposits  Subject  to 
Check  and  the  I']xtent  to  which  the  Present  Writer's 
exceed  or  pall  short  of  said  estimates. 


F.'s  Excess  (o 

R  Deficiency) 

A/TTTT'TTirT  r  *Q    T?ir^TTT  TH 

iVXli  LfUCjljLi  9    IXCjciV  LilO 

Unadjusted 

Adjusted 

1896 

2.69 

-.01 

+  .02 

1897 

2.75 

+  .05 

+  .11 

1898 

3.20 

-.01 

+  .02 

1899 

3.87 

+  .03 

+  .01 

1900 

4.21 

+  .19 

+  .23 

1901 

4.96 

+  .17 

+  .17 

1902 

5.37 

+  .06 

+  .03 

1903 

5.54 

+  .16 

+  .19 

1904 

5.85 

-.05 

-.08 

1905 

6.56 

-.02 

-.02 

1906 

6.86 

-.02 

-.05 

1907 

7.11 

+  .02 

+  .02 

1908 

6.52 

+  .08 

+  .05 

1909 

6.81 

-.06 

-.13 

1910 

7.71 

-.47 

-.48 

1911 

8.24 

-.46 

-.46 

APPENDIX    TO    THE    SECOND    EDITION,   ON 
"STANDARDIZING   THE   DOLLAR" 

The  plan  for  stabilizing  the  price  level  (and  therefore  the 
purchasing  power  of  money)  sketched  in  Chapter  XIII 
(pages  340-346)  in  relation  to  the  gold  exchange  standard  has 
been  more  fully  and  more  popularly  explained  since  this 
book  was  written.  (See,  e.g.,  Report  of  International  Con- 
gress Chambers  of  Commerce,  September  26,  1912 ;  Inde- 
pendent, January  2,  1913 ;  New  York  Times,  December  22, 
1912 ;  British  Economic  Journal,  December,  1912,  The 
most  complete  statement  is  that  in  The  Quarterly  Journal 
of  Economics,  February,  1913.) 

The  writer  also  hopes  soon  to  publish  a  book  devoted  to 
this  particular  subject. 

The  following  is  an  extract  from  an  address  in  Boston 
before  the  American  Economic  Association,  December,  1912, 
printed  in  the  American  Economic  Review  Supplement, 
March,  1913 :  — 

Briefly  stated,  the  plan  is  to  introduce  the  multiple  stand- 
ard, in  which  the  unit  is  a  "composite  ton"  or  "composite 
package"  of  many  staple  commodities,  not  of  course  by  us- 
ing such  a  package  in  any  physical  way  but  by  employing 
instead  its  gold  bullion  equivalent.  In  essence  it  would 
simply  vary  the  weight  of  gold  in  the  dollar  or  rather  behind 
the  dollar.  The  aim  is  to  compensate  for  losses  in  the 
purchasing  power  of  each  grain  of  gold  by  adding  the  neces- 
sary number  of  grains  of  gold  to  the  dollar. 

Both  on  the  basis  of  theory  and  of  facts, 'we  may  accept  as 
sound  the  principle  that  the  lighter  the  gold  dollar  the  less 
its  purchasing  power  and  the  more  magnified  the  scale  of 
prices ;  and  that  the  heavier  the  dollar  the  greater  its  pur- 
chasing power  and  the  more  contracted  the  scale  of  prices. 
Evidently  if  we  can  find  some  way  to  increase  the  weight  of 

494 


APPENDIX   TO   THE    SECOND   EDITION  495 

the  dollar  just  fast  enough  to  compensate  for  the  loss  in  the 
purchasing  power  of  each  grain  of  gold,  we  shall  have  a  fully 
"compensated  dollar,"  that  is,  a  dollar  which  has  constantly- 
restored  to  it  any  purchasing  power  it  may  lose  by  gold 
depreciation. 

We  now  have  a  dollar  of  fixed  weight  (25.8  grains),  but 
varying  purchasing  power.  Under  the  plan  proposed,  we 
should  have  a  dollar  of  fixed  purchasing  power,  but  varying 
weight. 

But  how  is  it  possible  to  have  a  dollar  of  varying  weight 
without  the  annoyance  of  a  constant  recoinage  of  gold  coin  ? 
Moreover,  if  this  can  be  done,  how  can  we  know  at  any  time 
what  weight  the  dollar  ought  to  have  without  leaving  this 
to  the  tender  mercies  of  some  political  official  ?  Here  are 
two  very  vital  questions. 

As  a  preparation  for  answering  these  two  questions,  it 
will  be  a  little  easier  to  explain  the  principle  of  the  proposal 
if  for  a  moment  we  assume  that  there  are  no  actual  gold 
coins  in  circulation,  but  only  gold  certificates.  This  sup- 
position is,  in  fact,  not  very  far  from  the  truth  in  the  United 
States ;  for,  outside  of  California,  there  is  very  little  actual 
gold  coin  in  circulation.  We  have  instead  nearly  a  billion 
dollars  of  gold  certificates  in  circulation,  representing  gold 
in  the  Treasury  of  the  United  States.  We  are  supposing 
for  the  moment  that  gold  circulates  in  no  other  way.  Under 
these  circumstances  it  is  evident  that  the  ultimate  gold 
dollar  is  out  of  sight  in  the  Treasury  of  the  United  States 
in  bars  of  gold  bullion.  Every  25.8  grains  of  this  gold  bul- 
lion is  a  virtual  dollar  behind  a  dollar  of  gold  certificates 
outstanding.  A  gold  bar  (of  standard  bullion)  weighing 
25,800  grains  virtually  contains  1000  gold  dollars. 

The  gold  miner  takes  such  bars  of  standard  gold  to  the 
mint  and  deposits  them  without  waiting  for  their  coinage, 
receiving  gold  certificates  in  return,  one  dollar  of  gold  cer- 
tificates for  each  25.8  grains  of  standard  gold  which  he  de- 
posits. On  the  other  hand,  holders  of  gold  certificates  may 
at  any  time  receive  gold  bullion  in  return,  when  they  desire 


496  THE    PURCHASING   POWER   OF   MONEY 

this  for  export,  or  for  use  in  the  arts  of  jewelry,  dentistry, 
gilding,  etc.,  receiving  25.8  grains  of  gold  for  each  dollar  of 
gold  certificates.  Thus  the  government  on  demand  gives 
or  takes  money  at  the  rate  of  25.8  grains  of  bullion  per 
dollar ;  the  virtual,  though  invisible,  dollar  being  this  25.8 
grains  of  gold  bullion,  nine-tenths  fine. 

The  proposal  here  made  is  to  change  the  weight  of  the 
dollar  as  an  offset  to  changes  in  value.  If  there  are  no  gold 
coins,  it  is  very  easy  to  do  this.  For  example,  if  there  should 
be  a  decrease  of  1  per  cent  in  the  value,  that  is,  purchasing 
power  of  gold,  then  the  weight  of  gold  bullion  which  consti- 
tutes the  virtual  dollar  would  be  declared  1  per  cent  greater, 
becoming  26.058  instead  of  25.8.  If  there  should  be  an 
increase  in  the  purchasing  power  of  gold,  the  weight  of  the 
virtual  dollar  would  be  reduced  accordingly.  Whenever  the 
gold  miner  took  gold  to  the  mint,  he  would  receive  a  gold 
certificate  not  necessarily  at  the  rate  of  one  dollar  for  each 
25.8  grains  of  standard  gold,  but  for  a  larger  or  smaller 
amount  as  the  case  might  be,  the  amount  always  being  that 
amount  which  would  possess  the  same  purchasing  power. 
Similarly  the  holder  of  gold  certificates  who  wishes  them 
redeemed  in  bullion  for  export  or  for  the  arts,  would  not 
always  get  exactly  25.8  grains  for  each  dollar  of  certificates, 
but  a  larger  or  smaller  sum,  as  the  case  might  be.  Thus  the 
government  would  be  receiving  gold  from  the  miner  and  giv- 
ing it  out  to  the  jeweler  just  as  at  present,  but  in  varying 
weights  per  dollar,  instead  of  at  the  arbitrarily  fixed  weight 
of  25.8  grains.  The  weight  of  gold  per  dollar  in  which,  at 
any  particular  time,  gold  certificates  were  redeemable  would 
constitute  the  virtual  and  only  gold  dollar.  Under  these 
circumstances  it  is  clear  that  it  would  be  entirely  feasible 
to  change  up  and  down  the  weight  of  the  gold  dollar  (that 
is,  the  amount  of  gold  bullion  interconvertible  with  a  dollar 
of  gold  certificates),  and  without  any  recoinage  or  other 
interference  with  the  outward  appearance  of  the  currency  in 
our  pockets. 

We  should  familiarize  ourselves  with  another  way  of  stat- 


APPENDIX   TO   THE    SECOND   EDITION  497 

ing  all  this.  Instead  of  saying  that  the  government  receives 
gold  bullion  at  the  mint  and  uses  this  for  redeeming  gold 
certificates,  we  may,  if  we  prefer,  say  that  the  government 
buys  and  sells  gold.  It  buys  gold  from  the  miner,  paying 
for  it  in  gold  certificates ;  it  sells  gold  to  the  jeweler,  who 
redeems  these  certificates.  At  present,  the  price  at  which 
gold  is  bought  and  sold  by  the  government  is  $18.60  an 
ounce  (for  standard  gold  nine-tenths  fine).  This  is  easily 
figured  out  from  the  weight  of  the  gold  dollar ;  for  25.8 
grains  of  gold  being  our  present  dollar,  each  ounce  (or  480 
grains)  of  gold  bullion  contains  480/25.8  or  18.60  virtual 
dollars.  To  say,  then,  that  we  now  have  a  fixed  weight  in 
our  gold  dollar,  25.8  grains,  is  the  same  thing  as  to  say  that 
we  have  a  fixed  government  price  for  gold,  $18.60  per  ounce. 
To  raise  the  weight  of  the  gold  dollar  1  per  cent,  or  from 
25.8  grains  to  26.058  grains,  is  the  same  thing  as  to  lower 
the  government  price  of  gold  from  $18.60  to  $18.42  per 
ounce. 

We  come  now  to  the  second  question :  How  would  it  be 
possible  to  know  the  proper  adjustments  to  be  made  in  the 
weight  of  the  virtual  dollar  —  the  gold  bullion  interconver- 
tible with  each  dollar  of  gold  certificates  —  without  putting 
a  dangerous  power  of  discretion  in  the  hands  of  government 
officials?  In  other  words,  how  can  the  adjustment  in  the 
weight  of  the  virtual  dollar  be  made  automatic?  The 
answer  is  :  By  means  of  statistics  called  "index  numbers  of 
prices."  Such  statistics  are  to-day  published  by  the  London 
Economist,  the  United  States  Bureau  of  Labor,  the  Canadian 
Department  of  Labour,  and  several  commercial  agencies,  such 
as  Bradstreet.  The  index  number  of  the  Bureau  of  Labor 
is  based  on  the  wholesale  prices  of  257  commodities,  and 
shows  from  year  to  year  the  extent  to  which  prices  on  the 
whole  advance  or  fall,  —  the  average  movement  of  all  the 
257  prices. 

There  are  various  systems  of  index  numbers,  but  they 
practically  all  agree  remarkably  well  with  each  other.  When 
once  a  system  of  index  numbers  is  decided  upon,  their  numer- 


498  THE    PURCHASING    POWER   OF   MONEY 

ical  calculation  becomes  a  purely  clerical  matter.  A  sta- 
tistical bureau  (as  for  instance  the  present  Bureau  of  Labor 
or  an  international  statistical  office)  would  compile  and 
publish  these  statistics  periodically  and  the  actual  prices  on 
which  they  were  based.  If  at  any  time  the  official  index 
number  showed  that  the  price  level  had  risen  1  per  cent  above 
par,  this  would  be  the  signal  for  an  increase  of  1  per  cent  in 
the  virtual  dollar. 

The  plan,  then,  is :  first,  to  provide  for  the  calculation  of 
an  official  index  number  of  prices ;  second,  to  adjust  corre- 
spondingly the  official  weight  of  the  virtual  dollar  at  which 
the  government  shall  issue  gold  certificates  to  miners  or 
redeem  them  for  jewelers,  in  other  words,  to  adjust  the  official 
prices  of  gold  at  which  the  government  stands  ready  to  buy 
or  sell  at  the  option  of  the  public. 

This,  then,  is  the  plan  in  brief  —  a  plan  virtually  to  mark 
up  or  down  the  weight  of  the  dollar  (that  is,  to  mark  down  or 
up  the  price  of  gold  bullion)  in  exact  proportion  to  the  devia- 
tions above  or  below  par  of  the  index  number  of  prices. 

A  few  additional  details  essential  to  the  working  of  the 
plan  may  now  be  briefly  mentioned.  You  are  still  waiting 
to  see  how  actual  gold  coin  could  be  used  in  such  a  system. 
To  be  continually  recoining  the  gold  in  circulation  would, 
of  course,  be  quite  impracticable.  But  this  would  be  un- 
necessary. Existing  gold  coin  would  remain  unchanged  at 
25.8  grains  per  dollar,  and  new  gold  coins  would  be  given 
the  same  weight.  Gold  coins  would  simply  become  what 
silver  dollars  now  are,  token  coins.  Or,  better,  they  would 
be,  like  the  gold  certificates,  mere  warehouse  receipts,  or,  as 
it  were,  "brass  checks"  for  gold  bullion  on  deposit  in  the 
Treasury.  Otherwise  expressed,  gold  coins  would  be  merely 
gold  certificates  printed  on  gold  instead  of  on  paper.  They 
would  be  used  exactly  as  gold  certificates  are  used  —  namely, 
issuable  to  the  gold  miner  in  return  for  his  bullion,  and 
redeemable  for  those  who  wished  bullion  for  export  or  in 
the  arts. 

The  excess  of  bullion  over  the  weight  of  the  coined  dollar 


APPENDIX   TO   THE    SECOND   EDITION  499 

itself  would  be  analogous  to  what  has  generally  been  called 
"  seigniorage"  ;  so  that  in  a  sense,  the  plan  may  be  described 
as  a  plan  to  restore  the  ancient  custom  of  seigniorage  on 
gold  coin.  Thus,  if  the  virtual  dollar  were  at  any  time 
35.8  grains,  the  excess  of  ten  grains  above  the  weight  of  the 
coin  dollar,  25.8  grains,  would  be  "seigniorage."  The  gold 
miner,  in  return  for  every  35.8  grains  of  standard  gold  bul- 
lion taken  to  the  mint,  would  receive,  at  his  option,  a  gold 
certificate  on  paper,  or  a  gold  certificate  on  gold  (that  is,  a 
dollar  gold  coin)  —  the  latter  containing,  just  as  at  present, 
25.8  grains.  Any  holder  of  gold  coin,  old  or  new,  and  any 
holder  of  gold  certificates  could  receive  from  the  govern- 
ment gold  bullion  at  the  official  rate  declared  from  time  to 
time.  He  would  thus  be  receiving  a  larger  quantity  of  gold 
bullion  than  the  amount  of  bullion  in  the  gold  dollar.  The 
gold  coin  would  then,  like  all  our  other  coins,  be  worth  more 
as  coin  than  as  bullion,  and  its  value  would  be  determined 
just  as  the  value  of  a  gold  certificate  or  any  other  paper 
money  is  to-day  determined,  by  the  ultimate  bullion  with 
which  it  would  be  interconvertible,  this  bullion  being  of 
greater  weight  than  the  weight  of  the  dollar  itself. 

The  only  real  complication  which  would  be  introduced 
by  allowing  gold  coin  to  remain  at  its  present  weight  and 
fineness  would  be  to  limit  the  operation  of  the  system  when 
prices  tended  to  fall  below  the  par  or  starting  point  at  which 
the  system  began.  The  weight  of  the  virtual  gold  dollar 
could  never  be  reduced  below  the  weight  of  the  coin  dollar ; 
for,  if  this  were  done,  the  seigniorage  would  become  a  minus 
quantity  and  all  the  gold  coin  would  be  immediately  melted 
into  bullion,  being  worth  more  melted  than  coined.  One 
proviso,  therefore,  in  the  system  would  be  that  the  weight 
of  the  virtual  dollar  should  never  be  less  than  25.8  grains 
and  that  therefore  the  government  price  of  gold  should  never 
be  more  than  $18.60  per  ounce.  Perhaps,  in  view  of  the 
present  dissatisfaction  with  high  prices,  many  people  would 
not  object  to  this  limitation  which  permits  prices  to  fall 
below  the  present  level,  but  does  not  permit  them  to  rise 


500  THE    PURCHASING   POWER   OF   MONEY 

further.  Yet  it  is  a  poor  rule  that  will  not  work  both  ways. 
Consequently,  while  I  personally  look  forward  to  an  upward 
tendency  of  prices  in  the  future,  the  possibility  of  a  downward 
movement  should  be  provided  for.  For  this  purpose,  gold 
coin  could,  if  desired,  be  recalled  at  the  outset  and  recoined 
in  lighter  weight,  just  as  the  Philippine  peso  was  recalled 
and  reduced  in  weight  when  the  recent  rise  in  the  price  of 
silver  threatened  to  lead  to  melting  the  silver  pesos.  But 
I  do  not  advocate  crossing  the  bridge  until  we  come  to  it. 
It  would  be  sufficient  to  provide  in  advance  for  crossing  it  in 
case  we  should  ever  come  to  it.  This  could  be  done  in  one 
of  two  ways.  It  could  be  provided  that,  if  ever  the  price 
level  should,  in  the  future,  sink  more  than,  say  10  per  cent 
below  the  original  par  or  price  level  from  which  the  system 
started,  all  gold  coins  should  then  be  withdrawn  from  cir- 
culation and  gold  certificates  employed  instead.  In  this  way 
we  should  be  rid  of  any  complication  from  the  use  of  gold 
coin,  and  would  be  at  liberty  forever  after  to  adjust  the 
weight  of  the  virtual  dollar  downward  as  well  as  upward. 
Or,  if  preferred,  it  could  be  arranged  that  when  prices  should 
sink  more  than  the  suggested  limit  of  10  per  cent  below  the 
original  level,  we  should  then  recoin  and  reduce  our  gold 
coins.  This  would  merely  mean  that  the  gold  on  which  we 
print  our  gold  certificates  would  be  reduced  in  weight.  It 
would  not,  of  course,  reduce  the  value  of  the  gold  coin  any 
more  than  the  reduction  in  the  weight  of  the  Philippine  peso 
which  was  made  for  a  similar  contingency  —  or,  to  take  an 
example  nearer  home,  the  reduction  of  10  per  cent  in  the 
weight  of  our  subsidiary  silver  coins  half  a  century  ago  — 
had  any  tendency  to  reduce  the  value  of  these  coins. 

If  the  latter  plan  were  chosen,  the  amount  of  reduction 
in  the  gold  coin  should  be  enough  to  provide  a  comfortable 
margin  for  any  similar  emergencies  in  the  future.  Any 
subsequent  recoinages  would  thus  be  deferred  a  long  time 
and  similar  provision  for  them  could  be  made.  Personally 
I  should  prefer  the  former  method,  eliminating  gold  coins 
altogether. 


APPENDIX   TO   THE    SECOND    EDITION  501 

Another  essential  detail  is  a  proviso  to  avoid  speculation  in 
gold  disastrous  to  the  government.  This  would  be  accom- 
plished by  means  of  a  slight  government  charge,  say  1  per 
cent,  for  minting.  This  charge,  which  existed  in  former 
days,  is  called  brassage.  It  would  mean  that  the  price  at 
any  particular  date  at  which  the  government  bought  gold 
would  be  slightly  less  than  the  price  at  which  it  sold  it. 
Without  such  a  margin  to  protect  the  government,  it  is 
evident  that  when  the  government  raised  its  price,  say  from 
$18  to  $18.10  an  ounce,  speculators  might,  in  anticipation 
of  this  rise,  buy  all  the  gold  in  the  government  vaults  at 
$18  in  order  to  sell  it  back  to  the  government  immediately 
after  the  change  in  price,  at  $18.10,  thus  profiting  ten  cents 
per  ounce  at  the  expense  of  the  government. 

Similarly,  a  fall  in  price,  say  from  $18.10  to  $18  per  ounce, 
would  encourage  the  opposite  form  of  speculation.  Holders 
of  bullion  would  then  rush  it  to  the  government  to  sell  it 
at  the  present  rate  of  $18.10,  and  immediately  after  the 
change  in  price,  buy  it  back  at  $18,  thus  profiting  again 
ten  cents  per  ounce  at  the  expense  of  the  government.  If, 
however,  the  government  were  protected  by  a  brassage  charge 
of  1  per  cent  and  if  it  were  provided  that  no  single  shift  in 
the  government  pair  of  prices,  whether  they  were  both  moved 
up  or  both  moved  down,  should  exceed  the  "brassage"  or 
margin  between  them,  it  is  clear  that  no  such  speculation 
could  occur,  for  there  would  be  a  greater  loss  from  the  pay- 
ments of  brassage  to  the  government  than  any  speculative 
gain  possible  from  the  change  in  price. 

Other  details  relate  to  the  provisions  for  establishing  and 
maintaining  a  gold  reserve  at  the  outset  where  no  such 
reserve  existed  in  the  first  place.  In  the  United  States  we 
could  utilize  the  50,000,000  ounces  of  gold  already  in  the 
Treasury  for  the  very  purpose  of  redeeming  the  $900,000,000 
of  gold  certificates  outstanding. 

We  have  standardized  every  other  unit  in  commerce 
except  the  most  important  and  universal  unit  of  all,  the  unit 
of  purchasing  power.     What  business  man  would  consent 


502  THE    PURCHASING   POWER   OF   MONEY 

for  a  moment  to  make  a  contract  in  terms  of  yards  of  cloth 
or  tons  of  coal,  and  leave  the  size  of  the  yard  or  the  ton  to 
chance  ?  Once  the  yard  was  the  girth  of  a  man.  In  order 
to  make  it  constant,  we  have  standardized  it.  We  have 
standardized  even  our  new  miits  of  electricity,  the  ohm,  the 
kilowatt,  the  ampere,  and  the  volt.  But  the  dollar  is  still 
left  to  the  chances  of  gold  mining.  At  first  we  could  not 
standardize  units  of  electricity  because  we  had  no  adequate 
instruments  for  measuring  those  elusive  magnitudes.  But 
as  soon  as  such  measuring  devices  were  invented,  these  units 
were  standardized.  We  have  hitherto  had  a  similar  excuse 
for  not  standardizing  the  dollar  as  a  unit  of  purchasing 
power,  and  so  a  standard  for  deferred  payments;  we  had 
no  instrument  for  measuring  it  or  device  for  putting  the 
results  in  practice.  With  the  development  of  index  numbers, 
however,  and  the  device  of  adjusting  the  seigniorage  accord- 
ing to  those  index  numbers,  we  now  have  at  hand  all  the 
materials  for  scientifically  standardizing  the  dollar  and  for 
realizing  the  long-coveted  ideal  of  a  "multiple  standard" 
of  value.  In  this  way  it  is  within  the  power  of  society,  when 
it  chooses,  to  create  a  standard  monetary  yardstick,  a 
stable  dollar. 


INDEX 


Aldrich  Report  on  Wholesale  Pricea, 

cited,  259,  260,  399. 
Aldrich-Vreeland  bill  of  1908,  146  n. 
American  colonies,  paper  money  in 

the,  256-258. 
Arrays,      use      of,      in      calculating 

quantities,   prices,   and  averages, 

355-362,  367-368. 
Arts,  influence  on  quantity  of  money 

of  consumption  of  gold  in  the,  103. 
Assets  of  bank,  must  be  adequate  to 

meet  liabilities,  38-39 ;  form  must 

be    such    as    to    meet    liabilities 

promptly,  42-47. 
Assignats,  experience  of  French  Rev- 

olurionists  with,   252-253. 
Atkinson,  F.  J.,  on  "Silver  Prices  in 

India."  243. 
Aupetit,  Albert,  cited,  157,  234,  237, 

240. 
Australia,  rise  of  prices  due  to  gold 

discoveries  in   (1851-1852),  241- 

242. 
Austria,    adoption   of  gold   standard 

by    (1892),    243;     experience    of, 

with     paper     money,     255-256 ; 

monetary  system  of,  referred  to, 

341-342,  344. 
Averages,  discussion  and  explanation 

of,  23-24,  198-203,  349-352. 


Bank  checks.     See  Checks. 

Bank  deposit  circulation,  before  and 
during  crises,  267-270.  <See  De- 
posit currency. 

Bank  deposits.     See  Deposits. 

"Bank  gold,"  115  n.'. 

Banking  laws,  relative  increase  in  de- 
posits partly  due  to  recent,   315. 

Bank  notes,  38-39 ;  circulation  of, 
before,  during,  and  after  crises, 
267-270. 


Barter,  the  exchange  of  goods  against 
goods,  13. 

Base,  selection  of  a,  in  constructing 
index  numbers,  203. 

Benefits  of  wealth,  meaning  of,  6 ; 
future  benefits  are  those  referred 
to,  6. 

Bills  of  exchange,  comparative  ad- 
justability of  prices  of,  186. 

Bimetallism,  mechanical  operation 
of,  115  ff. ;  two  requisites  of  com- 
plete :  free  and  unlimited  coinage 
of  both  metals  at  a  fixed  ratio, 
and  the  unlimited  legal  tender  of 
each  metal  at  that  ratio,  117; 
illustrations  of  workings  of,  by 
the  case  of  France  and  the  Latin 
Monetary  Union,  132-135 ;  the 
claim  that  prices  would  be 
steadied  by,  324-325 ;  shown  to 
be  an  indifferent  remedy  for  vari- 
ations in  price  level,  325-326 ; 
possibility  of  the  system  breaking 
down,  326  ;  possible  disruption  of 
prices  by  overvaluation  of  one 
metal  a  risk  to  be  feared,  327 ; 
limits  for  ratios  within  which  bi- 
metallism is  possible,  378. 

Bland-Alli.son  Act  of  1878,   142. 

Bolles,  Albert  S.,  cited,  257. 

Bonds,  prices  of,  among  least  ad- 
justable, 186-187  ;  effect  of  non- 
adjustability  of,  shown  in  super- 
sensitiveness  of   stocks,    190-192. 

Book  credit,  velocity  of  circulation 
increased  by,  81-83  ;  effect  of,  on 
equation  of  exchange,  370-371, 
491^92. 

Boom  periods  leading  to  crises,  58- 
67. 

Bortkiewicz,    L.   von,   cited,   32. 

Brace,  Harrison  H.,  Gold  Production 
and  Future  Prices  by,  cited,  80, 
241,  249. 

Brown,  Harry  G.,  cited,  37  n.,  65, 
212  n.»,  269,  426. 


503 


504 


INDEX 


Bullion,    influence    on    quantity    of 
money  of  melting  coin  into,  96-99. 
Business   barometers,   322,   478. 


California,  rise  of  prices  due  to  gold 
discoveries  in,   241-242. 

Capital,  defined  as  a  stock  of  goods 
existing  at  an  instant  of  time,  7 ; 
influence  of  accumulation  of,  on 
volume  of  trade,  76. 

"Charging,"  velocity  of  circulation 
increased  by,  81-83  ;  influence  of 
habit  of,  on  volume  of  deposits, 
88-89. 

Checks,  bank,  function  of,  33-35. 

Checks,  effect  of  use  of,  on  velocity 
of  circulation,  83 ;  increase  in, 
caused  by  increase  in  trade,  165 ; 
statistics  of  payments  by  (1909), 
305-306 ;  statistics  of  total  ex- 
change work  performed  by  (1896, 
1909),  317-318;  constitute  nine 
tenths  of  the  country's  transac- 
tions, 318  ;  method  of  calculating 
deposits  subject  to,   434-441. 

Checking  accounts,  statistics  of 
amounts  of,  from  1896-1909,  281- 
282,  491-492. 

Check  transactions  and  money  trans- 
actions, statistical  statement  of 
relative  importance  of,   317-318. 

Chili,  adoption  of  gold  standard  by 
(1895),  243. 

China,  rise  of  prices  in  (1874-1893), 
243-244. 

Circulating  credit,  or  bank  deposit 
currency,    33    S.     See   Deposits. 

Circulating  media,  classification  of, 
in  United  States,  12-13.  See 
Currency. 

Circulation,  statistics  of  money  in 
circulation  from  1896-1909,  280- 
281.     See  Velocity  of  circulation. 

Circulation  of  bank  notes  and  bank 
deposits  before  and  at  times  of 
crises,  267-270. 

Circulation  of  money,  signifies  the 
aggregate  amount  of  its  transfers 
against  goods,  13  ;  general  practi- 
cal formula  for  calculating,  448- 
460 ;  application  of  formula  to 
calculation  of  circulation  during 
1896-1909,  460  ff. 


Clark,  J.  B.,  cited,  221. 

Coefficient  of  correlation,  application 
of,  294-296. 

Coin-transfer  concept  of  velocity,  353. 

Commerce,  foreign  compared  with 
internal,  305-306,  484-486. 

Committee  of  British  Association  for 
Advancement  of  Science,  report 
of  on  index  numbers,  228-229. 

Commodities,  defined,  2 ;  com- 
parative adjustability  of  prices  of, 
186-187 ;  changes  in  quantities 
of,  corresponding  to  changes  in 
prices,  194-195 ;  types  of,  con- 
trasted, 382-384. 

Conant,  Charies  A.,  cited,  132,  140, 
223. 

Confederate  States,  value  of  gold  and 
index  numbers  of  prices  in  the, 
263-265. 

Continental  paper  money,   257-258. 

Contracts,  restriction  of  free  move- 
ment of  prices  because  of,  185, 
189 ;  nonadjustability  of  prices 
varies  with  length  of,  189 ;  meas- 
urement of  appreciation  or  depre- 
ciation of  loan  contracts,  by  use 
of  index  numbers,   208-225. 

Costa  Rica,  adoption  of  gold  stand- 
ard by   (1896),   243. 

Cost  of  living,  rise  in,  concluded  to 
be  merely  a  part  of  general  move- 
ment of  prices,  316. 

Credit,  circulating,  or  bank  deposit 
currency,  33  ff. 

Credit  cycle,  history  of  a,  58-72 ; 
table  of  statistics  illustrating  cul- 
mination of  a,  271-273  ;  lessening 
of  fluctuations  by  tabular  stand- 
ard of  value  plan  of  regulating 
price  level,  335. 

"Crime  of  73,"  the,  141. 

Crises,  the  culmination  of  an  up- 
ward price  movement,  65 ;  be- 
lated adjustment  of  rate  of 
interest  as  a  factor  in,  66 ;  corre- 
spondence between  circulation, 
private  deposits,  and,  265-270 ; 
conditions  preceding,  266 ;  a 
crisis  defined  as  an  arrest  of  the 
rise  of  prices,  266 ;  international 
character  of,  266-270. 

Currency,  or  circulating  media,  de- 
fined as  any  type  of  property  right 
which  serves  as  a  means  of  ex- 


INDEX 


505 


change,  10 ;  two  chief  classes : 
money  and  bank  deposits  subject 
to  check,  10 ;  bank  deposits,  33  ff. 
See  Deposits. 


D 


Darwin,  Leonard,  Bimetallism  by, 
cited,  127. 

D'Avencl,  Vicomte,  estimates  by, 
cited,  234,  237. 

Deferred  payments,  use  of  index 
numbers  for  measuring  apprecia- 
tion or  depreciation  of,  208-225. 

De  Launay,  The  World's  Gold  by, 
cited,  98. 

Del  Mar,  History  of  the  Precious 
Metals  by,   cited,   237,   239. 

Demand,  difference  between  effects 
of  an  increased,  for  an  individual 
commodity  and  of  an  increased 
general  demand  for  goods,    180. 

Demonetization  of  silver,  lowering 
of  prices  in  gold-standard  countries 
by,  242-245. 

Density  of  population,  effects  of  in- 
creased, on  velocity  of  circulation 
and  on  volume  of  trade,  164-166, 
315. 

Deposits,  bank  (deposit  currency), 
influence  of,  on  equation  of  ex- 
change and  hence  on  purchasing 
power,  33  ff. ;  quantitative  rela- 
tion of,  to  money  in  a  given  com- 
munity, 51-52,  151 ;  expansion 
of,  during  periods  of  rising  prices, 
58-60,  273 ;  contraction  of,  in 
period  of  falling  prices,  67-70 ; 
velocity  of  circulation  of,  increases 
with  density  of  population,  87 ; 
dependence  of,  on  quantity  of 
money,  162  ;  effects  of  change  in 
ratio  between  quantity  of  money 
and,  162-163 ;  increase  in,  will 
have  no  appreciable  effect  on 
velocities  of  circulation  and 
volume  of  trade,  but  will  raise 
prices  slightly,  163-164 ;  effects 
on  prices  of  changes  in  (with 
special  attention  to  crises  and 
depressions),  265  ff. ;  statistics  of 
amounts  of,  from  1896-1909,  281- 
285 ;  proved  to  have  tripled,  and 
velocity  of  circulation  of,  to  have 
increased  50  per  cent  in  fourteen 


years,  304-305 ;  statistics  of 
amount  per  capita  and  velocity 
of  circulation  (1909),  305;  growth 
of,  shown  to  be  a  large  factor  in 
raising  prices,  307-311  ;  chief 
causes  of  increase  in,  315  ;  velocity 
of  circulation  of,  chiefly  due  to 
concentration  of  population,  315; 
description  of  method  of  calculat- 
ing,  434-441. 

Depression,  causes  of  period  of,  58— 
67,    71-72.     See   Crises. 

Dewey,  Davis  Rich,  cited,  258 ;  use 
of  the  median  for  wages  by,  428. 

Dispersion  of  prices,  184  ff. ;  caused 
by  previous  contract,  legal  re- 
strictions, and  custom,  185-189 ; 
by  nonvariation  of  articles  related 
to  the  money  metal,  189-190 ; 
by  variation  of  individual  prices 
under  influence  of  law  of  supply 
and  demand,    190-194. 

Drobisch,  M.  W.,  cited,  396. 

Dunbar,  Theory  and  History  of  Bank- 
ing by,  cited,  35. 


E 


Economics,  defined  as  the  science  of 
wealth,    1. 

Ecuador,  adoption  of  gold  standard 
by     (1899),     243. 

Edgeworth,  F.  Y.,  cited,  25  n.",  167, 
199,  218,  220,  325,  328,  334,  392, 
396,  397.  423,  426,  427. 

Egypt,  adoption  of  gold  standard  by 
(1885),  243. 

England,  statistics  of  price  move- 
ments in,  238-240 ;  account  of 
experience  of,  with  paper  money, 
238-239,  253-255;  dates  of  fi- 
nancial crises  in,  267. 

England,  Minnie  Throop,  statistics 
by,    cited,    174,   273. 

Equation  of  exchange,  defined  as 
the  equation  between  a  stream 
of  transferred  rights  in  goods  and 
an  equivalent  stream  of  trans- 
ferred money  or  money  substi- 
tutes, 7  ;  is  a  statement  in  mathe- 
matical form  of  the  total  trans- 
actions effected  in  a  certain  period 
in  a  given  connmunity,  15-16  ;  the 
money  side  and  the  goods  side, 
16-17 ;      the     magnitude     called 


506 


INDEX 


velocity  of  circulation  or  rapid- 
ity of  turnover,  17  ;  arithmetical 
illustration  of,  17-21 ;  mechani- 
cal illustration  of,  21-24 ;  alge- 
braic statement  of,  24-28,  364, 
368 ;  influence  of  bank  deposit 
currency  on,  33  ff. ;  application 
of,  to  bank  deposits  or  circulating 
credit,  48^9 ;  disturbance  of, 
during  periods  of  transition,  55 
ff. ;  implies  no  causal  sequence, 
149-150 ;  statistical  verification 
of,  276-318 ;  construction  of 
index  numbers  required  by,  198 
S.  (see  Index  numbers) ;  benefits 
€o  business  men  of  a  fuller  knowl- 
edge of,  322-323;  effect  of  time 
credit  on,  370-371 ;  modification 
of,  required  by  international 
trade,  372-375. 

Essars,  Pierre  des,  cited,  63,  87,  269, 
270. 

Evelyn,  Sir  G.  S.,  early  attempt  to 
construct  series  of  index  numbers 
by,  208  n.    t 

Exchange,  defined  as  consisting  of 
two  mutual  and  voluntary  trans- 
fers of  wealth,  3.  »See  Equation 
of  exchange. 

Exchangeability,  quality  of,  which 
makes  a  commodity  money,  9 ; 
differing  degrees  of,  found  in  real 
estate,  mortgages  on  real  estate, 
corporation  securities,  govern- 
ment bonds,  bills  of  exchange, 
sight  drafts,  and  checks,  9-10. 

Exchanges,  classification  of,  into  ex- 
change of  goods  against  goods 
(barter),  of  money  against  money 
(changing  money),  and  of  money 
against  goods  (purchase  and  sale), 
13. 

Expectation,  results  of,  on  prices, 
262-263. 


Failures,  causes  leading  to  commer- 
cial, 64-67. 

Fairchild,  F.  R.,  article  by,  cited,  193. 

Falkner,  Roland  P.,  index  numbers 
of,  229. 

Farm  lands,  value  of,  affected  by 
changes  in  rate  of  interest,  193. 

Fetter,  Frank,  cited,  221. 

Fiars  prices,  Scotch,  334. 


Fiduciary  money,  definition  of,  11. 

Fisher,  Irving,  The  Nature  of  Capi- 
tal  and  Income  by,  cited,  1,  44, 
214;  The  Rate  of  Interest  by, 
cited,  56,  57,  58,  65,  70,  210,  214, 
216,  224,  266  ;  papers  and  articles 
by,  25  n.2.  115,  174,  190,  210,  211, 
244.  384. 

Fleetwood,  Bishop  William,  work  by, 
cited,  208  n. 

Flow  or  stream  of  goods,  distinction 
between  stock  or  fund  of  goods 
and,  7 ;  three  classes  of  economic 
flows,  besides  income,  7. 

Flux,  A.  W.,    cited,  423. 

Food,  rise  of  wholesale  prices  of, 
compared  with  general  change  in 
prices,  316. 

Forecasts,  economic,  321-322. 

Foreign  trade,  influence  of,  on  quan- 
tity of  money,  90-96 ;  volume  of, 
contrasted  with  internal,  305- 
306,  484-486. 

Forest  land,  sensitiveness  of  value  of, 
to  changes  in  rate  of  interest,  193. 

Foxwell,  H.  S.,  cited,  218. 

France,  experience  with  bimetallism 
in,  132-135  ;  experiences  of,  with 
paper-money  schemes,  252-253 ; 
dates  of  financial  crises  in,  267. 

Freedom  of  trade,  effect  of,  on 
volume  of  trade  and  price  level, 
77-78.     See  Tariff. 


Geographical  influence  on  volume  of 
trade,  75. 

"George  Smith's  money,"  47. 

Germany,  adoption  of  gold  standard 
by  (1871-1873),  242-243. 

Giffen,  Robert,  cited,  206,  392. 

Gold,  the  best  example  of  a  money 
commodity,  2  ;  comparative  non- 
adjustability  of  prices  of  articles 
made  of,  187,  189-190 ;  statistics 
of  increase  in  annual  production 
of,  235-236 ;  continued  increase 
in  prices  predicted,  due  to  in- 
crease in  production  of,  248-249  ; 
increasing  output  of,  249  ;  statis- 
tical comparison  of  greenbacks 
and,  259 ;  difficulties  of  finding 
substitute  for,  as  a  medium,  323- 
324;     various    proposed    substi- 


INDEX 


507 


tutes :  bimetallism,  polymetal- 
lism,  convertible  paper  currency, 
tabular  standard  of  value,  com- 
bination of  gold-exchange  stand- 
ard and  tabular  standard,  etc., 
324-348 ;  variabilities  of  pro- 
duction of  silver  and,  326  n. 

Gold  bullion  and  gold  coin,  equal 
values  of,  97-99. 

Gold  coin,  the  only  primary  money 
in  the  United  States,  13. 

Gold-exchange  standard,  system  of 
partial  redeemability  known  as, 
131-132,  337  ff. ;  in  British  India, 
138-140;  in  the  Philippines, 
Mexico,  and  Panama,  140. 

Gold  mining,  chief  cause  of  increase 
of  money,  315. 

Gold  standard,  general  adoption  of, 
and  resultant  fall  of  prices  (1873- 
1896),  242-243. 

Goodbody,  Robert,  article  by,  cited, 
188. 

Goods,  definition  of  the  term,  6. 

Greenbacks,  issuance  of,  in  United 
States,  141 ;  a  useless  anomaly, 
145 ;  depreciation  of,  258-260 ; 
comparison  of  prices  in  gold  and 
in  (1861-1879),  259;  explanation 
of  value  of,  found  in  expectation 
of  redemption,  261. 

Gresham's  Law,  that  cheap  money 
will  drive  out  dear  money,  112  flf. 

Griswold,  Robert  N.,  calculations  by, 
484. 

H 

Hadley,  A.  T.,  Economics  by,  cited, 

25  n.2. 
Hardy,  S.  M.,  paper  by,  mentioned, 

277  n.2. 
Hazard,   Thomas,    Account  Book  of, 

quoted,  256-257. 
Hertzka,  joint-metallism  scheme  of, 

328. 
Hickernell,  W.  F.,  table  by,  146,  147. 
Hildebrand,  work  by,  cited,  161. 
Holt,  Byron  W.,  cited,  186. 
Hunt,     William    C.,    estimates    by, 

465-467. 


Income,    definition    of,    as    flow    of 
benefits    from     stock     of     goods 
(capital),  7. 
2k 


Index  number,  use  of  an,  to  stand 
for  prices  taken  collectively  (P), 
184  ;  to  stand  for  volume  of  trade 
(T),   195-196. 

Index  numbers,  a  necessity  owing 
to  dispersion  of  prices,  184-196 ; 
comparison  of,  as  to  form,  198  fif. ; 
simple  or  unweighted  averages, 
198-199  ;  weighted  averages,  199- 
203 ;  methods  of  constructing, 
200-202;  selection  of  the  base, 
203  ;  the  successive  base  or  chain 
system,  203-204 ;  selection  of 
prices,  204  ff. ;  use  of,  to  measure 
capital  and  to  measure  income, 
205 ;  to  measure  six  subclassifi- 
cations,  205-206  ;  use  of,  to  serve 
as  basis  of  loan  contracts,  or 
standard  of  deferred  payments, 
208  ff. ;  report  of  committee  of 
British  Association  for  Advance- 
ment of  Science,  228-229;  ad- 
vantages of  the  median  over 
other  forms  of,  230-231 ;  index 
numbers  of  prices  from  1896- 
1909,  290-293,  486-487 ;  of  vol- 
ume of  trade  from  1896-1909, 
290,  478  ff. ;  use  of,  in  tabular 
standard  of  value  plan  for  con- 
trolling price  level,  332-337  ;  each 
form  of  index  number  for  prices 
demonstrated  to  imply  a  correl- 
ative form  of  index  number  for 
quantities,  385-391 ;  eight  tests  for 
a  good  index  number,  400-417. 

India,  experience  of,  with  the  limp- 
ing standard,  138-140 ;  adoption 
of  gold  standard  by  (1893),  243; 
resultant  rise  of  prices  in,  243-244. 

Inflation,  rate  of  interest  raised  by, 
57-58. 

Insolvency  in  banking,  43. 

Insufficiency  of  cash,  condition  of, 
at  banks,  43-45. 

Interest.     See  Rate  of  interest. 

International  trade,  modification  of 
equation  of  exchange  required  by, 
90-96,  372-375. 

Invention,  as  a  disturbing  force  to  the 
financial  equilibrium,  70 ;  in- 
fluence of,  on  volume  of  trade  and 
price  level,  77. 

Irredeemable  paper  money,  effects  of, 
on  prices,  238-239,  250  £F.  Se4 
Paper  money. 


508 


INDEX 


Italy,  the  case  of  an  overissue  of  paper 
money  in,  114. 


Jacob,  William,  cited,  237. 

Japan,  adoption  of  gold  standard  by 
(1897),  243;  resultant  rise  of 
prices  in,    243-244. 

Jevons,  W.  S.,  cited,  8,  9,  12,  80,  88, 
186,  195,  237  n.,  241,  249,  254, 
332,  335,  397;  quoted  on  diffi- 
culties of  determining  velocity  of 
circulation  of  money,  286 ;  claim 
of,  that  a  bimetallic  standard 
would  tend  to  steady  prices,  325. 

Johnson,  J.  F.,  Money  and  Currency 
by,  cited,   136,  251,  333. 

Joint-metallisms,    schemes    of,    328. 

Juglar,  Clement,  cited,  65  n.^,  266, 
267,  269,  270. 


Kemmerer,  E.  W.,  works  by,  cited, 
14  n.,  25  n.2,  4.'S,  139,  140,  213, 
226,  279,  282,  331,  487;  pioneer 
work  of,  in  testing  statistically 
the  quantity  theory,  276-278, 
430-432. 

Kinley,  Money  by,  cited,  60,  87,  212 ; 
Credit  Instruments,  226,  444,  462 ; 
original  statistical  work  of,  282- 
283,  461-462,  491-492. 

Knapp,  G.  F.,  cited,  32. 

Knowledge  of  technique  of  produc- 
tion, influence  on  volume  of  trade, 
76. 

L 

Labor,   influence   of   division   of,    on 

volume  of  trade,  75. 
Labor  standard  of  purchasing  power 

of  money,  proposed,  222. 
Labor  unions,  inability  of,  to  affect 

general   price   level,    179-180. 
Lake,    A.    C,    pamphlet    by,    cited, 

347  n. 
Landry,   Adolphe,   cited,   84,   85. 
Latin  Monetary  Union,  the,  134-135. 
Lauck,  cited,  269. 
Laughlin,  work  by,  cited,  14  n.,  50  n., 

140,  242  n.2 ;  quoted,  104  n.,  165  n. 
Launay,  L.  de,  cited,  248. 
Law,  John,  paper-money  scheme  of, 

252. 


Legal  tender,  what  constitutes,  8. 

Leslie,  Clifife,  cited,  236. 

"Limit  of  tolerance"  of  mints,  114— 
115. 

"Limping"  standard,  monetary  sys- 
tem called,  127 ;  the  gold-ex- 
change standard  a  kind  of,  131— 
132 ;  experience  of  British  India 
with,  138-140;  in  the  United 
States,  140-148;  Walras's  gold 
standard  with  a  "silver  regulator" 
a  variant  of,   328-329. 

Loan  contracts,  measurement  of  ap- 
preciation or  depreciation  of,  by 
index  numbers,  208  ff.  See  Con- 
tracts. 

Logan,  Walter  S.,  article  by,  cited, 
188. 

Loss,  influence  on  quantity  of  money 
of  consumption  of  gold  by,  103. 

Lowe,  Joser,h,  suggestion  of  use  of 
index  number  or  tabular  stand- 
ard of  value  by,  208  n.,  332. 

M 

Macleod,  H.  D.,  History  of  Economics 
by,  cited,  112. 

Magee,  J.  D.,  figures  of,  on  world's 
production  of  gold  and  silver, 
235  n.,  241. 

Mandats,  French  paper  money,  suc- 
cessors  to   the   assignats,    253. 

Marginal  cost  of  production,  ex- 
planation of,   99-101. 

Marshall,  Alfred,  Principles  of  Eco- 
nomics by,  quoted,  71-72  ;  system 
called  symmetallism  suggested  by, 
328;    cited,   423. 

Massachusetts,  paper  money  in 
colonial,    256. 

Median,  advantages  of,  over  other 
forms  of  index  numbers,  230-231, 
425-428. 

Menger,  work  by,  cited,  5. 

Merriam,   Lucius  S.,  cited,  221. 

Mexico,  adoption  of  gold  standard 
by    (1905),    243. 

MUl,  J.  S.,  cited,  25  n.^,  31,  102, 
200. 

Mining  land,  value  of,  as  affected 
by  changes  in  rate  of  interest, 
193. 

Minting  and  melting,  influence  of, 
on  quantity  of  money,  96-99. 


INDEX 


509 


Mitchell,  W.  C,  works  by,  cited,  141, 
200,  268,  259,  260,  265,  426,  486 ; 
use  of  the  median  for  price  in- 
dexes, 428. 

Money,  definition  of,  aa  any  com- 
modity generally  acceptable  in 
exchange,  2,  8  ;  three  meanings  of: 
in  the  sense  of  wealth,  in  the  sense 
of  property,  and  in  the  sense  of 
written  evidence  of  property 
right  (bank-notes,  checks,  stock 
certificates,  etc.),  5;  "circula- 
tion" of,  consists  of  a  stream  of 
transferred  money  or  money  sub- 
stitutes, 7 ;  use  of  gold  dust  and 
gold  nuggets,  tobacco,  wampum, 
shells,  etc.,  for,  8-9  ;  quality  of 
exchangeability  which  makes,  9- 
10  ;  distinction  between  bank  de- 
posits subject  to  check  and  bank 
notes,  11 ;  money  rights  are  what 
a  payee  accepts  without  question, 
by  legal-tender  laws  or  well- 
established  custom,  1 1  ;  primary 
and  fiduciary  money,  11-12; 
circulation  of,  siginfies  the  ag- 
gregate amount  of  its  transfers 
against  goods,  13 ;  the  purchas- 
ing power  of,  is  indicated  by  the 
quantities  of  other  goods  which 
a  given  quantity  of  money  will 
buy,  13-14 ;  bank  notes,  38-39, 
47 ;  Gresham's  Law,  that  cheap 
money  will  drive  out  dear  money, 
112  ff. ;  comparison  of  stocks  of, 
in  Europe,  and  price  levels,  237- 
238 ;  statistics  of  money  in  cir- 
culation from  1896-1909,  280- 
281,  430-434;  shown  to  have 
nearly  doubled  in  fourteen  years, 
304-305 ;  statistics  of  actual  cir- 
culation of,  305-306 ;  statistical 
statement  of  check  and  cash  trans- 
actions, 317-318,  491-492;  sub- 
stitutes for,  unlike  other  sub- 
stitutes, 376-377.  See  also  Quan- 
tity of  money. 

Money  changing,  the  exchange  of 
money   against   money,    13. 

Money  famines,  causes  of,  67-69. 

Morawetz,  Victor,  cited,  45. 

Mortgage  notes,  prices  of,  among 
least    adjustable,    186-187. 

Muhleman,  Maurice  L.,  calculations 
of,   245,   433-434. 


Mulhall,  Dictionary  of  Statistics,  cited, 
240. 

N 

National  Bank  notes.  United  States, 
145-146. 

Netherlands,  adoption  of  gold  stand- 
ard  by   (1875-1876),    243. 

Newcomb,  Simon,  Principles  of 
Political  Economy  by,  25  n.'. 

Nicholson,  J.  S.,  cited,  206,  392. 

Nitti,  cited,  199. 

Nogaro,   Bertrand,   cited,   32,    127. 

Norton,  J.  Pease,  cited,  59 ;  index 
numbers  of,  230. 

O 

Oresme,  Nicolas,  112. 
Orient,    regarded    aa    the    "  sink    of 
silver,"  236,  247. 


Pair  of  prices  device,  343-344. 

Palgrave,  Dictionary  of  Political 
Economy  by,  cited,  8. 

Panics  and  their  causes,   64-66. 

Paper  money,  slight  influence  on 
prices  of  the  English  irredeem- 
able (1801-1820),  238-240;  usual 
effects  of  redeemable  and  of  irre- 
deemable, on  prices,  250  ff.  ;  pre- 
carious value  of,  251-252 ;  ex- 
periences of  various  countries  with, 
252  ff. ;  John  Law's  scheme,  252  ; 
account  of  England's  experience 
with,  253-255 ;  in  Austria,  255- 
256  ;  American  Continental,  257— 
258 ;  experience  of  United  States 
with,  258-203  ;  Confederate,  263- 
265 ;  redeemable,  suggested  as  a 
price-steadying  plan,  331-332. 

Pareto,  work  by,  cited,  70. 

Pars,  readjustment  of  gold,  undei 
author's  proposed  plan  for  reg- 
ulating price  level,  341->342, 
344-345. 

Pearson,  Karl,  the  "correlation  co- 
efficient" of,  294. 

Persons,  Professor,  cited,  278-279, 
294. 

Person-turnover  concept  of  velocity, 
353,    362-363. 

Peru,  adoption  of  gold  standard  by 
(1897),  243. 


510 


INDEX 


Philippines,  buying  and  selling  ex- 
change in  the,  337,  338. 

Polyinctallism,  proposed  scheme  for 
steadying  monetary  standard, 
327-328. 

Population,  increased  density  of, 
quickens  flow  of  money  and 
checks,  164-165 ;  changes  in 
volume  of  trade  and  velocity  of 
circulation  caused  by  changes  in 
density  of,  165-166 ;  concentra- 
tion of,  the  chief  cause  of  increase 
of  velocity  of  circulation,  315. 

Porter,  Morgan,  calculations  by,  326 
n. 

Price,  L.  L.,  Money  and  its  Relation 
to  Prices  by,  cited,  235,  237,  241. 

Price  level,  dependent  on  three  sets 
of  causes :  quantity  of  money  in 
circulation,  "efficiency"  or  ve- 
locity of  circulation,  and  volume 
of  trade,  14  ;  the  quantity  theory, 
that  prices  vary  in  direct  propor- 
tion to  quantity  of  money,  14, 
157-159,  296-297 ;  varies  directly 
as  the  quantity  of  money  in  cir- 
culation, directly  as  the  velocity 
of  circulation,  inversely  as  the 
volume  of  trade  done  by  it,  29 ; 
effect  on,  of  doubling  the  denomi- 
nations of  all  money,  29-30 ;  of 
debasing  the  currency,  30 ;  of 
doubling  the  coinage,  30-31 ; 
effects  of  rising  and  of  falling,  on 
rate  of  interest,  56  ff. ;  history 
of  a  period  of  rising,  leading  to  a 
crisis,  58-67 ;  the  corresponding 
downward  course  of,  67-70 ;  out- 
side influences  which  tend  to 
lower :  geographical  differences 
in  natural  resources,  division  of 
labor,  improved  productive  tech- 
nique, and  accumulation  of  capi- 
tal, 74-76 ;  lowering  of,  by 
changes  in  human  wants,  76-77 ; 
lowering  of,  by  increased  trans- 
portation facilities,  relative  free- 
dom of  trade,  development  of 
eflBcient  monetary  and  banking 
systems,  and  business  confidence, 
77-79 ;  increase  of,  by  book 
credit,  81-83  ;  raising  of,  by  den- 
sity of  population  and  increased 
transportation  facilities,  88 ;  regu- 
lation   of,    by   international    and 


interlocal  trade,  90-96 ;  workings 
of  a  protective  tariff  in  regard  to, 
93-95,  312-314;  restatement  of 
truth  that  the  normal  effect  of 
an  increase  in  the  quantity  of 
money  is  an  exactly  proportional 
increase  in  the,  157-159 ;  slight 
effect  of  changes  in  volume  of 
trade  on,  166-169;  held  not  to 
be  an  independent  cause  of 
changes  in  any  of  the  other  mag- 
nitudes in  equation  of  exchange, 
169  ff. ;  normally  the  one  abso- 
lutely passive  element  in  the 
equation  of  exchange,  172 ;  em- 
phasis laid  on  distinction  between 
individual  prices  relative  to  each 
other  and  the  price  level,  175  ;  not 
determined  by  individual  prices, 
175-180 ;  inability  of  trusts  or 
labor  combinations  to  affect,  179- 
180 ;  increased  general  demand 
for  goods  results  in  a  lower,  180 ; 
effect  of  dispersion  of  prices,  184— 
197 ;  general  trend  upward  of, 
234 ;  influence  on,  of  discovery 
of  America  and  increase  in  pro- 
duction of  gold  and  silver,  235- 
236 ;  comparison  of  metallic 
stocks  in  Europe  at  various  dates 
and,  237-238  ;  summary  of  move- 
ments of,  during  nineteenth  cen- 
tury, 240-242  ;  rapid  rise  of,  from 
1789-1809,  240-241 ;  fall  of,  to 
two  fifths,  between  1809-1849, 
241 ;  rise  of  by  one  third  to  one 
half,  in  1849-1873,  241-242; 
lowering  of,  from  1873  to  1896, 
242 ;  effect  on,  of  general  adop- 
tion of  gold  standard,  242-243; 
effect  on  silver  countries  of  adop- 
tion of  gold  standard  in  other 
countries,  243-245 ;  rise  in,  from 
1896  to  present,  245-246;  con- 
tinued rise  in,  predicted,  due  to 
increase  in  gold  production,  248- 
249 ;  effects  on,  of  changes  in 
deposit  currency,  265  ff. ;  con- 
clusion that  expansion  of  deposit 
currency  raises,  rather  than  that 
rise  of  prices  creates  deposit  cur- 
rency, 273  ;  statistics  of,  as  shown 
by  index  numbers  of  general 
prices  from  1896-1909,  291-292; 
importance  of  appreciating  exist- 


INDEX 


511 


ence  of  a  law  of  direct  proportion 
between  quantity  of  money  and, 
296-297  ;  shown  to  have  risen  by 
two  thirds,  in  fourteen  years 
(1896-1909),  304-305;  summing- 
up  concerning  rise  of  and  causes, 
from  1896-1909,  307;  discussion 
and  analysis  of  the  separate  fac- 
tors concerned  in  rise  of,  307-311 ; 
conclusion  as  to  importance  of 
increase  of  money  as  a  factor  in 
price-raising,  311 ;  full  effect  of 
quantity  of  money  on,  not  felt 
on  account  of  overflow  to  foreign 
countries,  311-312;  question  as 
to  whether  price  level  is  control- 
lable, 319  ff. ;  proposed  methods 
of  maintaining  a  stable  level :  by 
bimetallism,  324-327;  by  poly- 
metallism,  327-328;  by  sym- 
metallism,  joint  metallism,  and 
other  purely  academic  schemes, 
328-329  ;  by  inconvertible  paper 
money,  329 ;  by  a  var3dng  seign- 
iorage charge,  330-331 ;  by 
convertible  paper  currency,  re- 
deemable on  demand,  331-332; 
by  a  tabular  standard  of  value 
plan,  332-337  ;  by  gold-exchange 
standard  combined  with  tabular 
standard,  337-346 ;  changes  in 
individual  prices  demonstrated 
not  to  affect,  necessarily,  382- 
384. 

Prices,  individual :  method  of  ob- 
taining a  price,  3 ;  dispersion  of, 
184  ff.  ;  index  numbers  of,  184, 
486-487  ;  nonadjustment  of  some, 
causes  greater  ratio  of  change  in 
others,  185  ff. ;  of  contracts,  cus- 
tom, and  legal  restrictions,  185, 
187-189 ;  classification  of  goods 
according  to  adjustability  of 
prices,  186-187 ;  narrow  range 
of  variation  in,  of  articles  made 
of  money  metal,  189-190  ;  factors 
working  through  law  of  supply 
and  demand  which  affect,  192- 
194 ;  effect  on,  of  changes  in  rate 
of  interest,  193  ;  impossibility  of 
a  uniform  change  in,  194-195 ; 
changes  in  quantities  of  commodi- 
ties with  changes  in,  194-195. 

Primary  money  vs.  fiduciary  money, 
11-12. 


Production,  influence  of  knowledge 
of  technique  of,  on  volume  of 
trade,  76. 

Property,  or  property  right,  defined 
as  the  right  to  enjoy  the  services 
or  benefits  of  wealth,  4 ;  distinc- 
tion between  wealth  and,  4 ; 
units  for  the  measurement  of, 
4-5  ;  distinction  between  property 
rights  and  the  certificates  of  those 
rights,  5. 

Purchase  and  sale,  the  exchange  of 
money  against  goods,  13. 

Purchasing  power  of  money,  as  re- 
lated to  the  equation  of  exchange, 
8  ff. ;  is  indicated  by  the  quan- 
tities of  other  goods  which  a  given 
quantity  of  money  will  buy,  13- 
14  ;  influence  of  deposit  currency 
on,  33  ff. ;  disturbance  of,  during 
transition  periods,  55-73 ;  vari- 
ous indirect  influences  on,  — 
conditions  of  production  and 
consumption,  individual  habits, 
foreign  trade,  melting  and  mining, 
etc.,  74  ff. ;  influence  of  monetary 
systems,  112-148;  influence  of 
quantity  of  money,  149  ff. ;  index 
numbers  of,  184-233 ;  problem 
of  making  more  stable,  319-348. 
See  Price  level. 

Q 

Quantities  of  commodities,  changes 
in,  corresponding  to  changes  in 
prices,  194-195,  382-384. 

Quantity  of  money,  relation  of  prices 
to,  14,  157-159,  296-297  (see 
Quantity  theory) ;  deposit  cur- 
rency normally  proportioned  to, 
49-53 ;  increase  in,  a  cause  of 
disturbance  to  financial  equilib- 
rium, 70;  causes  outside  the 
equation  of  exchange  that  affect, 
90  ff. ;  influence  of  foreign  trade, 
90-96 ;  influence  of  melting  and 
minting,  96-99  ;  influences  operat- 
ing through  the  production  and 
consumption  of  money  metals, 
99-104 ;  influence  of  monetary 
systems,  112  ff. ;  doubling  of, 
will  double  deposits,  will  not 
affect  velocity  of  circulation,  but 
will  increase  prices  in  proportion 


512 


INDEX 


to  its  own  increase,  151-159  ;  the 
law  of  direct  proportion  between 
quantity  of  money  and  price 
level,  157-159,  296-297;  ratio 
between  deposits  and,  162  ;  effect 
on,  of  changes  in  velocities  of  cir- 
culation, 164-165  ;  effects  on,  of 
changes  in  volume  of  trade,  165 ; 
proof  of  importance  of,  as  a  price- 
raising  factor,  307-311 ;  full  effect 
of  increase  in,  not  felt  in  United 
States  because  of  overflow  abroad, 
311-312;  causes  working  toward 
increase  of,  315. 

Quantity  theory  of  money,  that  prices 
vary  proportionately  to  money, 
14,  157-159,  296-297;  causes 
leading  to  contesting  of  this 
theory,  14-15 ;  the  equation  of 
exchange,  15-31  (see  Equation  of 
exchange)  ;  three  illustrations  of, 
29-31 ;  dependent  on  the  fact 
that  money  has  no  power  to 
satisfy  human  wants  except  a 
power  to  purchase  things  which 
do  have  such  power,  32  ;  in  causal 
sense,  151  ff.  ;  does  not  hold 
strictly  true  during  transition 
periods,  159-162. 

Quarries,  effect  on  value  of,  of 
changes  in  rate  of  interest,  193. 


R 


Railways,  influence  of,  on  velocity  of 
circulation,  88. 

Rate  of  interest,  determination  of, 
in  banking,  45  ;  effects  of  rising 
and  falling  prices  on,  56-58,  266 
n.i ;  the  outstripping  of,  by  prices 
in  period  of  rising  prices,  59-60, 
271-273 ;  commercial  crises  due 
to  belated  adjustment  of,  66,  71- 
72 ;  tardiness  of  lowering  of,  in 
period  of  falling  prices,  68  ;  effect 
of  changes  in,  on  individual  prices, 
193  ;  adjustment  of,  not  sufficient 
to  compensate  for  fluctuations  in 
value  of  money,  223,  232-233. 

Real  estate,  scope  of,  as  a  class  of 
wealth,  1-2 ;  comparative  ad- 
justability of  price  of  rented,  186  ; 
prices  of  leased,  among  the  least 
adjustable,  186  ;  value  of,  affected 
by   changes   in   rate   of   interest, 


193  ;  small  part  taken  by,  in  total 
business  transactions  of  United 
States,  226. 

Receipts  and  disbursements,  effect 
on  velocity  of  circulation  of  in- 
creased frequency  of,  83-85 ; 
effect  of  regularity  of,  85-86. 

Reserves,  banking,  45  ff . ;  legal  regu- 
lation of,  46 ;  effect  of  rising 
prices  on,  64-65 ;  ratio  which 
exists  between  quantity  of  money, 
amount  of  deposits,  and,  162. 

Retail  prices,  data  concerning  com- 
parative importance  and  adjust- 
ability of,  226-227. 

Rhode  Island,  paper  money  in 
colonial,  256-257. 

Ricardo,  theory  of  equation  of  ex- 
change launched  by,  25  n.* ; 
cited,  31  n.,  44,  188,  250,  343. 

Robertson,  J.  Barr,  articles  by,  cited, 
244  n.  2,  245. 

Ross,  Edward  A.,  cited,  221. 

"Runs  on  banks,"  caused  by  period 
of  rising  prices,  65. 

Russia,  adoption  of  gold  standard  by 
(1897),  243. 


Sakata,  translation  by,  243  n.  *. 

Salaries,  relative  adjustability  of, 
regarded  as  one  of  class  of  prices, 
187. 

Sauerbeck,  statistics  by,  cited,  238- 
240,  242. 

Scandinavian  monetary  union,  adop- 
tion of  gold  standard  by,  243. 

Schwab,  J.  C,  Confederate  States  oj 
America  by,  quoted,  263-265. 

Scott,  Money  a7id  Banking  by,  quoted, 
15  n. 

Scrope,  G.  P.,  use  of  index  number 
to  indicate  standard  of  value  sug- 
gested by,  208  n.,  332. 

Seager,  Introduction  to  Economics  by, 
cited,  144  n. 

Seasonal  changes,  effects  of,  on  ve- 
locity of  circulation,  quantity  of 
money  and  deposits,  72,  161. 

Sea-water  gold,  249. 

Sedgwick,  H.,  cited,  200. 

Seigniorage,  charge  for  changing  bul- 
lion into  coin,  98 ;  regulation  of 
supply  of  metallic  money  by  a 
varying,  proposed,  330-331. 


INDEX 


513 


Shaler,  N.  S.,  quoted,  324. 

Shaw,  W.  A.,  History  of  the  Currency 
by,  cited,  133,  134,  136. 

Sherman  Act  of  1890,  142-143. 

Short  crops,  as  a  disturbing  force  to 
the  financial  equilibrium,  70. 

Siberia,  effect  of  introduction  of  gold 
from,  241. 

Silver,  statistics  of  increase  in  annual 
production  of,  235-236  ;  variabili- 
ties of  production  of  gold  and, 
326  n. ;  danger  from  overvalua- 
tion of,  in  case  bimetallism  were 
a  standard,  327. 

Silver  certificates  in  United  States, 
143-145. 

Silver  countries,  effect  on,  of  adop- 
tion of  gold  standard  by  other 
countries,  243-245. 

Simple  averages,  198-199. 

Smiley,  W.  Y.,  mentioned,  484. 

Smith,  J.  Allen,  cited,  335. 

Soetbeer,  Adolf,  figures  of,  on  world's 
production  of  gold  and  silver, 
235  n.,  237. 

Sprague,  O.  M.  W.,  editor  Dunbar's 
Theory  and  History  of  Banking, 
35  ;    cited,  269  n. ». 

Stock  of  goods,  distinction  between 
flow  of  goods  and,  7. 

Stocks,  adjustability  of  prices  of,  187  ; 
supersensitiveness  of,  to  monetary 
fluctuations,  190-192 ;  trans- 
actions in  listed  securities  con- 
stitute eight  per  cent  of  country's 
business,  226. 

Stokes,  joint-metallism  scheme  of, 
328. 

Substitutes,  prices  of,  move  in  sym- 
pathy with  prices  of  articles 
themselves,  189-190 ;  substitutes 
for  money  unlike  other  substi- 
tutes, 376-377. 

Sumner,  W.  G.,  cited,  8,  9,  255,  256. 

Supply  and  demand,  factors  working 
through  principle  of,  which  affect 
individual  prices,  192-194. 

Symmetalism,  system  called,  328. 


Tabular  standard  of  value  plan  for 
controlling  price  level,  332-337 ; 
main  objections  to,  335-337  ;  com- 
bination of  plan  with  the  gold-ex- 


change standard,  suggested,  338- 
346. 

Tariff,  effects  of,  on  purchasing 
power  of  money,  93-95 ;  tem- 
porary effect  of  a  protective,  to 
raise  price  level  of  protected 
country,  312;  afterward  ceases 
to  affect  price  level,  except  for  its 
interfering  effect,  312-313;  con- 
sideration of  tariffs  of  1897  and 
1909,  313-314. 

Technical  knowledge,  influence  of,  on 
volume  of  trade  and  price  level,  76. 

Telegraph,  velocity  of  circulation  in- 
creased by  the,  88. 

Tests  for  index  numbers,  400-417. 

Thom,  De  Courcy  W.,  cited,  266, 
267,  268. 

Thrift,  influence  of,  on  velocity  of  cir- 
culation, 79-81. 

Timber  land,  effect  on  value  of,  of 
changes  in  rate  of  interest,    193. 

Time,  the  element  of,  and  relation 
of  wealth,  property,  and  benefits 
to,   6-7. 

Time  of  turnover,  concept  of,  354, 
363. 

Tithe  averages  in  England,   333. 

Tokens,  forms  of  fiduciary  money 
called,    12. 

Trade,  defined  as  a  flow  of  transfers, 
7 ;  influence  of  foreign,  on  quan- 
tity of  money,  90-96  ;  volumes  of 
foreign  and  domestic  compared, 
305-306,  484-486.  See  Volume 
of  trade. 

Transfer  of  wealth,  defined  as  a 
change  of  its  ownership,   3. 

Transition  periods,  temporary  effects 
of,  on  equation  of  exchange,  55 
ff. ;  characterized  by  rising  or  by 
falling  prices,  56 ;  effect  of,  on 
equation  of  exchange,  159-162. 
See   Crises. 

Transportation  facilities,  effect  of, 
on  volume  of  trade,  77 ;  relation 
between  velocity  of  circulation 
and,   88,    166. 

Trusts,  inability  of,  to  affect  the 
general  price  level,   179-180. 

Turnover,  rapidity  of,  17 ;  rates  of 
individual,  dependent  on  volume 
of  expenditure,  167 ;  statistics  of, 
at  Yale  University,  37^-382.  Set 
Velocity  of  circulation. 


514 


INDEX 


U 


United  States,  sketch  of  monetary 
system  of,  140  ff. ;  issuance  of 
greenbacks,  141 ;  complicated 
and  objectionable  features  of 
monetary  system,  143  ff. ;  ex- 
perience of,  with  paper  money, 
258-263  ;  dates  of  financial  crises 
in,  267. 

Unweighted  averages,  198-199,  349- 
352. 

Uses  of  wealth,  to  be  distinguished 
from  utility  of  wealth,  6. 

Utility  standard  of  purchasing  power 
of  money,  220-222. 


Value,  the  magnitude  called,  and 
its  determination,  3  ;  is  the  price 
of  any  item  of  wealth  multiplied 
by  its  quantity,   3-4. 

Velocity  of  circulation,  dependence 
of  price  level  on,  14  ff. ;  definition 
of,  17,  352  ff. ;  causes  outside  the 
equation  of  exchange  which  affect, 
79-89  ;  increase  of,  by  habit  of 
"charging,"  or  book  credit,  81- 
83 ;  increase  of,  by  use  of  checks 
rather  than  money,  83 ;  increase 
of,  by  increased  frequency  of  re- 
ceipts and  disbursements,  83-85 ; 
effect  of  regularity  of  receipts  and 
disbursements,  85-86 ;  increased 
by  density  of  population,  87,  315  ; 
affected  by  extent  and  speed  of 
transportation,  88  ;  proved  to  be 
unaffected  by  quantity  of  money 
or  of  deposits,  151-154  ;  changes 
in  velocities  affect  prices  but  not 
quantity  of  money  or  volume  of 
trade,  164-165 ;  effects  on,  of 
increase  in  volume  of  trade,  165- 
168 ;  before,  during,  and  after 
crises,  270 ;  statistics  relative  to 
that  of  bank  deposits  from  1896- 
1909,  282-285 ;  statistics  of  circu- 
lation of  money  from  1896-1909, 
285-290 ;  velocity  of  circulation 
of  money  proved  to  have  in- 
creased only  10  per  cent  in  thirteen 
years,  304-305 ;  of  money  shown 
to  be  twenty-one  times  a  year, 
(1909),      305-306;       of     deposit 


currency  shown  to  be  fifty-three 
times  a  year  (1909),  305;  of 
money  shown  to  be  a  negligible 
factor  in  raising  prices,  307-311 ; 
of  deposits  a  large  factor  in  raising 
prices,  307-311;  discussion  of 
concept  of,  352—354  ;  coin-trans- 
fer and  person-turnover  concepts 
of,  353,  362-363 ;  time  of  turn- 
over concept,  354,  363 ;  method 
of  calculating  velocity  of  circula- 
tion  of   deposits,  441-446. 

Venezuela,  adoption  of  gold  standard 
by  (1896),  243. 

Volume  of  trade,  dependence  of  price 
level  on,  14,  18-21,  24  ff. ;  causes 
outside  the  equation  of  exchange 
which  affect:  geographical  dif- 
ferences, division  of  labor,  extent 
and  variety  of  human  wants,  etc., 
74-79  ;  proved  to  be  independent 
of  quantity  of  money  (except  in 
transition  periods),  155-156;  in- 
crease in,  increases  money  in 
circulation,  165 ;  effects  of,  on 
velocity  of  circulation,  165-168 ; 
statistics  of,  from  1896-1909,  290- 
291,  304-306;  method  of  calcu- 
lating (1896-1909),  478  ff.  ;  in- 
dex numbers  of,  479. 


W 


Wages,  effect  of  frequency  of  pay- 
ment of,  on  velocity  of  circula- 
tion, 83-85 ;  relative  adjustability 
of,  considered  as  prices,  186-187  ; 
obtaining  a  true  index  number 
for,  207-208;  amount  to  three 
per  cent  of  total  business  transac- 
tions in  United  States,  226. 

Walker,  Francis  A.,  works  by,  cited, 
8,    11,    251,    265,    333. 

Walras,  scheme  of  a  gold  standard 
with  a  silver  regulator  suggested 
by,  328-329. 

Walsh,  C.  M.,  cited,  199,  208  n., 
223,  225,  393,  394,  396,  397, 
398. 

Wealth,  defined  as  material  objects 
owned  by  human  beings,  1 ;  two 
essential  attributes  of,  materiality 
and  appropriation,  1 ;  classifica- 
tion of,  under  three  heads,  real 
estate,  commodities,  and  human 


INDEX 


515 


beings,  1-2  ;  possibDity  of  measur- 
ing, in  physical  units,  2-3  ;  trans- 
fer, exchange,  price  and  value  of, 
defined,  3—4 ;  ownership  of,  or 
property,  4;  meaning  of  "bene- 
fits of  wealth,"  6. 

Weighted  averages,  199-203,  349- 
352. 

Wells,  David  A.,  referred  to,  176. 

White,  Andrew  D.,  Paper  Money 
Inflation  in  France  by,  cited, 
252. 

White,  Horace,  Money  and  Banking 
by,  cited,  47. 


Wicksell,  Knut,  article  by,  cited,  59, 

60. 
Workmen,    relative   adjustability   of 

price  of  servicea  of,   186-187. 


Yale  University,  statistics  of  rapidity 
of  individual  turnover  at,  167, 
379-382. 

Z 

Zizek,  Frans,  work  by,  cited,  349. 
Zuckerkandl,  cited,  14  n. 


Printed  in  the  United  States  of  America. 


V 


A; 


'"X 


\   ,/v 


^i'                  UNIVERSITY  OF  CALIFORNIA  LIBRARY 
Los  Angeles       i 
This  book  is  DUE  on  the  lasd  daU  iCaniped  below. 

•fgfcWsTS 

DEC    9l§^ 

iL  Aj'f'''/"'""' 

APR  07 1986 

OCT  09  W<ife 

Form  L9-Series  444 

UWIVEKSITY  OF  CALIFOKNIA 

AT 

LOS  ANGELES 

LIBRARY 


gp 


3  1158  00001  9678 


HG 

F5:p 

1911 
cop. 2 


UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 


AA    000  987  203     7 


^muyyji^m^aHiigjmii; 


